{"id":97038,"date":"2026-08-28T22:56:31","date_gmt":"2026-08-28T14:56:31","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/97038.html"},"modified":"2026-08-28T22:56:31","modified_gmt":"2026-08-28T14:56:31","slug":"%e4%bb%8e%e4%b8%80%e9%81%93gesp%e7%9c%9f%e9%a2%98%e5%87%ba%e5%8f%91%ef%bc%9a%e8%81%8a%e8%81%8a%e6%9c%89%e9%99%90%e5%b0%8f%e6%95%b0%e7%9a%84%e8%b4%a8%e5%9b%a0%e5%ad%90%e5%88%a4%e5%ae%9a%e5%ae%9a","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/97038.html","title":{"rendered":"\u4ece\u4e00\u9053GESP\u771f\u9898\u51fa\u53d1\uff1a\u804a\u804a\u6709\u9650\u5c0f\u6570\u7684\u8d28\u56e0\u5b50\u5224\u5b9a\u5b9a\u7406"},"content":{"rendered":"<p>\u9898\u6e90&#xff1a;\u6d1b\u8c37 P15798 [GESP202603 \u4e94\u7ea7] \u6709\u9650\u4e0d\u5faa\u73af\u5c0f\u6570<\/p>\n<p>\u5c0f\u65f6\u5019\u5b66\u5206\u6570\u7684\u65f6\u5019&#xff0c;\u8001\u5e08\u544a\u8bc9\u6211\u4eec <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         1<\/p>\n<p>         2<\/p>\n<p>        &#061;<\/p>\n<p>        0.5<\/p>\n<p>       \\\\frac{1}{2} &#061; 0.5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.5<\/span><\/span><\/span><\/span><\/span> \u662f\u6709\u9650\u5c0f\u6570&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         1<\/p>\n<p>         3<\/p>\n<p>        &#061;<\/p>\n<p>        0.333<\/p>\n<p>        \u2026<\/p>\n<p>       \\\\frac{1}{3} &#061; 0.333\\\\ldots<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.333<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\">\u2026<\/span><\/span><\/span><\/span><\/span> \u662f\u65e0\u9650\u5faa\u73af\u5c0f\u6570\u3002\u4f46\u4f60\u6709\u6ca1\u6709\u60f3\u8fc7&#xff1a;\u4e3a\u4ec0\u4e48\u504f\u504f\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>       2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        5<\/p>\n<p>       5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u80fd\u8ba9\u5c0f\u6570&#034;\u505c\u4e0b\u6765&#034;&#xff1f;\u5982\u679c\u7ed9\u4f60\u4e00\u4e2a\u8303\u56f4&#xff0c;\u6bd4\u5982\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>       2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        11<\/p>\n<p>       11<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">11<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4f60\u80fd\u5feb\u901f\u6570\u51fa\u6709\u591a\u5c11\u4e2a&#034;\u80fd\u8ba9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         1<\/p>\n<p>         a<\/p>\n<p>       \\\\frac{1}{a}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">a<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span> \u53d8\u6210\u6709\u9650\u5c0f\u6570&#034;\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u5417&#xff1f;<\/p>\n<p>\u8fd9\u9053\u9898\u6765\u81ea 2026 \u5e74 3 \u6708 GESP \u4e94\u7ea7\u8ba4\u8bc1&#xff0c;\u8868\u9762\u4e0a\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u533a\u95f4\u8ba1\u6570\u9898&#xff0c;\u5b9e\u9645\u4e0a\u5b83\u8003\u5bdf\u7684\u662f\u6570\u8bba\u4e2d&#034;\u6709\u9650\u5c0f\u6570\u5224\u5b9a\u5b9a\u7406&#034;\u7684\u5de5\u7a0b\u5316\u5e94\u7528\u3002\u672c\u6587\u5c06\u5e26\u4f60\u4ece\u5341\u8fdb\u5236\u7684\u672c\u8d28\u51fa\u53d1&#xff0c;\u7406\u89e3\u4e3a\u4ec0\u4e48\u5206\u6bcd\u53ea\u80fd\u542b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>       2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        5<\/p>\n<p>       5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5e76\u628a\u8fd9\u4e2a\u601d\u60f3\u6c89\u6dc0\u6210\u4e00\u4e2a\u53ef\u4ee5\u590d\u7528\u7684\u5224\u5b9a\u6a21\u677f\u3002<\/p>\n<h3>\u4e00\u3001\u95ee\u9898\u672c\u8d28&#xff1a;\u5c0f\u6570\u80fd\u4e0d\u80fd&#034;\u505c&#034;&#xff0c;\u5206\u6bcd\u8bf4\u4e86\u7b97<\/h3>\n<p>\u5f88\u591a\u540c\u5b66\u62ff\u5230\u8fd9\u9053\u9898&#xff0c;\u7b2c\u4e00\u53cd\u5e94\u662f&#034;\u679a\u4e3e\u6bcf\u4e2a\u6570&#xff0c;\u7136\u540e\u505a\u9664\u6cd5\u770b\u80fd\u4e0d\u80fd\u9664\u5c3d&#034;\u3002\u8fd9\u4e2a\u601d\u8def\u5728\u6570\u636e\u8303\u56f4\u5c0f\u7684\u65f6\u5019\u6ca1\u95ee\u9898&#xff0c;\u4f46\u5982\u679c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        R<\/p>\n<p>       R<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span> \u8fbe\u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         10<\/p>\n<p>         12<\/p>\n<p>       10^{12}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">12<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u9664\u6cd5\u6a21\u62df\u5c31\u5f7b\u5e95\u5931\u6548\u4e86\u3002\u6240\u4ee5\u6211\u4eec\u9700\u8981\u56de\u5230\u6570\u5b66\u672c\u8d28&#xff0c;\u627e\u5230\u4e0d\u4f9d\u8d56\u4e8e\u5177\u4f53\u9664\u6cd5\u8fd0\u7b97\u7684\u5224\u5b9a\u65b9\u6cd5\u3002<\/p>\n<p>\u5173\u952e\u5b9a\u7406\u662f\u8fd9\u6837\u7684&#xff1a;\u4e00\u4e2a\u6700\u7b80\u5206\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          p<\/p>\n<p>          q<\/p>\n<p>        \\\\frac{p}{q}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.2286em;vertical-align: -0.4811em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7475em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.4461em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">p<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4811em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span> \u80fd\u5316\u4e3a\u6709\u9650\u5c0f\u6570&#xff0c;\u5f53\u4e14\u4ec5\u5f53\u5206\u6bcd <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         q<\/p>\n<p>        q<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span> \u7684\u8d28\u56e0\u6570\u5206\u89e3\u4e2d\u53ea\u5305\u542b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         2<\/p>\n<p>        2<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         5<\/p>\n<p>        5<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u4e3a\u4ec0\u4e48&#xff1f;\u56e0\u4e3a\u5341\u8fdb\u5236\u7684\u57fa\u6570\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        10<\/p>\n<p>        &#061;<\/p>\n<p>        2<\/p>\n<p>        \u00d7<\/p>\n<p>        5<\/p>\n<p>       10 &#061; 2 \\\\times 5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">10<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">2<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>\u3002\u4efb\u4f55\u6709\u9650\u5c0f\u6570\u90fd\u53ef\u4ee5\u5199\u6210 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         k<\/p>\n<p>          10<\/p>\n<p>          n<\/p>\n<p>       \\\\frac{k}{10^n}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.2251em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8801em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5935em\"><span class=\"\" style=\"top: -2.786em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5f62\u5f0f&#xff08;\u6bd4\u5982 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        0.125<\/p>\n<p>        &#061;<\/p>\n<p>         125<\/p>\n<p>         1000<\/p>\n<p>        &#061;<\/p>\n<p>         1<\/p>\n<p>         8<\/p>\n<p>       0.125 &#061; \\\\frac{125}{1000} &#061; \\\\frac{1}{8}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.125<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1000<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">125<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">8<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002\u5f53\u6211\u4eec\u628a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         1<\/p>\n<p>         a<\/p>\n<p>       \\\\frac{1}{a}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">a<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span> \u901a\u5206\u6210\u8fd9\u79cd\u5f62\u5f0f\u65f6&#xff0c;\u5206\u6bcd\u5fc5\u987b\u80fd\u6574\u9664\u67d0\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         10<\/p>\n<p>         n<\/p>\n<p>       10^n<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6644em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6644em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u800c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         10<\/p>\n<p>         n<\/p>\n<p>        &#061;<\/p>\n<p>         2<\/p>\n<p>         n<\/p>\n<p>        \u00d7<\/p>\n<p>         5<\/p>\n<p>         n<\/p>\n<p>       10^n &#061; 2^n \\\\times 5^n<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6644em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6644em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7477em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6644em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6644em\"><\/span><span class=\"mord\"><span class=\"mord\">5<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6644em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6240\u4ee5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u53ea\u80fd\u7531 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>       2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        5<\/p>\n<p>       5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u7ec4\u6210\u3002<\/p>\n<p>\u8fd9\u9053\u9898\u7684\u6838\u5fc3\u7279\u5f81\u53ef\u4ee5\u6982\u62ec\u4e3a\u4ee5\u4e0b\u51e0\u70b9&#xff1a;<\/p>\n<ul>\n<li>\u6570\u5b66\u5b9a\u7406\u9a71\u52a8&#xff1a;\u4e0d\u662f\u6a21\u62df\u9664\u6cd5&#xff0c;\u800c\u662f\u7528\u6570\u8bba\u5b9a\u7406\u76f4\u63a5\u5224\u5b9a<\/li>\n<li>\u56e0\u5b50\u5265\u79bb\u6cd5&#xff1a;\u901a\u8fc7\u53cd\u590d\u9664\u4ee5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         2<\/p>\n<p>        2<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         5<\/p>\n<p>        5<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5c06&#034;\u5408\u6cd5&#034;\u8d28\u56e0\u5b50\u5168\u90e8\u53bb\u9664<\/li>\n<li>\u5224\u5b9a\u5373\u8ba1\u6570&#xff1a;\u5224\u5b9a\u51fd\u6570\u8db3\u591f\u9ad8\u6548\u65f6&#xff0c;\u53ef\u4ee5\u76f4\u63a5\u904d\u5386\u533a\u95f4\u8ba1\u6570<\/li>\n<li>\u8d2a\u5fc3\u9664\u5c3d\u7b56\u7565&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         2<\/p>\n<p>        2<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         5<\/p>\n<p>        5<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u4e92\u8d28&#xff0c;\u9664\u7684\u987a\u5e8f\u4e0d\u5f71\u54cd\u7ed3\u679c<\/li>\n<li>\u9002\u7528\u8303\u56f4\u5e7f&#xff1a;\u8be5\u5b9a\u7406\u9002\u7528\u4e8e\u4efb\u610f\u5206\u6570\u7684\u6700\u7b80\u5f62\u5f0f\u5224\u5b9a<\/li>\n<\/ul>\n<p>\u6240\u4ee5\u8fd9\u9053\u9898\u7684\u672c\u8d28\u662f&#xff1a;\u628a&#034;\u6709\u9650\u5c0f\u6570&#034;\u8fd9\u4e00\u6570\u8bba\u6982\u5ff5&#xff0c;\u8f6c\u5316\u4e3a&#034;\u8d28\u56e0\u5b50\u53ea\u542b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         2<\/p>\n<p>        2<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         5<\/p>\n<p>        5<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>&#034;\u7684\u53ef\u5224\u5b9a\u6761\u4ef6\u3002<\/p>\n<h3>\u4e8c\u3001\u89e3\u9898\u7b56\u7565&#xff1a;\u9664\u5c3d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>       2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        5<\/p>\n<p>       5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u770b\u8fd8\u5269\u4ec0\u4e48<\/h3>\n<p>\u9762\u5bf9&#034;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u7684\u8d28\u56e0\u5b50\u662f\u5426\u53ea\u542b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>       2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        5<\/p>\n<p>       5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>&#034;\u7684\u5224\u5b9a\u95ee\u9898&#xff0c;\u6700\u81ea\u7136\u7684\u601d\u8def\u662f\u56e0\u5b50\u5265\u79bb&#xff1a;<\/p>\n<p>\u6b65\u9aa4\u4e00&#xff1a;\u9664\u5c3d\u6240\u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         2<\/p>\n<p>        2<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span>\u3002\u7528 while (x % 2 &#061;&#061; 0) x \/&#061; 2; \u628a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u4e2d\u6240\u6709\u7684\u56e0\u5b50 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>       2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u5168\u90e8\u9664\u6389\u3002<\/p>\n<p>\u6b65\u9aa4\u4e8c&#xff1a;\u9664\u5c3d\u6240\u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         5<\/p>\n<p>        5<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>\u3002\u7528 while (x % 5 &#061;&#061; 0) x \/&#061; 5; \u628a\u5269\u4f59\u7684\u56e0\u5b50 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        5<\/p>\n<p>       5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u5168\u90e8\u9664\u6389\u3002<\/p>\n<p>\u6b65\u9aa4\u4e09&#xff1a;\u68c0\u67e5\u7ed3\u679c\u3002\u5982\u679c\u5269\u4e0b\u7684\u6570\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>       1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8bf4\u660e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u53ea\u7531 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>       2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        5<\/p>\n<p>       5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u7ec4\u6210&#xff1b;\u5982\u679c\u5269\u4e0b\u5927\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>       1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8bf4\u660e\u8fd8\u6709\u5176\u4ed6\u8d28\u56e0\u5b50&#xff08;\u6bd4\u5982 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        3<\/p>\n<p>       3<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span>\u3001<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        7<\/p>\n<p>       7<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span>\u3001<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        11<\/p>\n<p>       11<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">11<\/span><\/span><\/span><\/span><\/span> \u7b49&#xff09;&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         1<\/p>\n<p>         a<\/p>\n<p>       \\\\frac{1}{a}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">a<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span> \u5fc5\u7136\u662f\u65e0\u9650\u5faa\u73af\u5c0f\u6570\u3002<\/p>\n<p>\u8fd9\u4e2a\u7b56\u7565\u7684\u5de7\u5999\u4e4b\u5904\u5728\u4e8e&#xff1a;\u6211\u4eec\u4e0d\u9700\u8981\u77e5\u9053 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         a<\/p>\n<p>        a<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u7684\u5b8c\u6574\u8d28\u56e0\u6570\u5206\u89e3&#xff0c;\u53ea\u9700\u8981\u786e\u8ba4&#034;\u9664\u4e86 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         2<\/p>\n<p>        2<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         5<\/p>\n<p>        5<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u4e4b\u5916\u6ca1\u6709\u5176\u4ed6\u8d28\u56e0\u5b50&#034;\u3002\u8fd9\u5c31\u50cf\u4f60\u68c0\u67e5\u4e00\u4e2a\u888b\u5b50\u91cc\u662f\u5426\u53ea\u6709\u7ea2\u7403\u548c\u84dd\u7403\u2014\u2014\u4f60\u4e0d\u9700\u8981\u6570\u6e05\u695a\u6bcf\u79cd\u7403\u5404\u6709\u591a\u5c11\u4e2a&#xff0c;\u53ea\u9700\u8981\u628a\u7ea2\u7403\u548c\u84dd\u7403\u5168\u90e8\u62ff\u51fa\u6765&#xff0c;\u770b\u770b\u888b\u5b50\u91cc\u8fd8\u6709\u6ca1\u6709\u5269\u4e0b\u7684\u7403\u3002<\/p>\n<h3>\u4e09\u3001\u7b97\u6cd5\u6a21\u677f&#xff1a;\u56e0\u5b50\u5265\u79bb\u5224\u5b9a\u6cd5<\/h3>\n<h4>3.1 \u7b97\u6cd5\u5230\u5e95\u5728\u5e72\u4ec0\u4e48&#xff1f;\u2014\u2014 \u76f4\u89c9\u89e3\u91ca<\/h4>\n<p>\u56e0\u5b50\u5265\u79bb\u6cd5\u7684\u6838\u5fc3\u601d\u60f3\u53ef\u4ee5\u7528\u4e00\u53e5\u8bdd\u6982\u62ec&#xff1a;\u628a\u5206\u6bcd\u4e2d\u6240\u6709&#034;\u5341\u8fdb\u5236\u7684\u5408\u6cd5\u57fa\u56e0&#034;&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         2<\/p>\n<p>        2<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         5<\/p>\n<p>        5<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>&#xff09;\u5168\u90e8\u5254\u9664&#xff0c;\u770b\u770b\u8fd8\u6709\u6ca1\u6709&#034;\u975e\u6cd5\u6b8b\u7559&#034;\u3002\u5b83\u5c31\u50cf\u4e00\u4f4d\u4e25\u683c\u7684\u5b89\u68c0\u5458&#xff0c;\u53ea\u5141\u8bb8\u643a\u5e26 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>       2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u53f7\u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        5<\/p>\n<p>       5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u53f7\u7269\u54c1\u901a\u8fc7&#xff0c;\u5176\u4ed6\u4e00\u5f8b\u6263\u4e0b\u3002<\/p>\n<p>\u5728\u672c\u9898\u4e2d&#xff0c;\u5b89\u68c0\u6d41\u7a0b\u53d8\u6210&#xff1a;<\/p>\n<li>\u68c0\u67e5\u7269\u54c1\u4e2d\u6709\u6ca1\u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         2<\/p>\n<p>        2<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u53f7\u7269\u54c1&#xff0c;\u6709\u5c31\u5168\u90e8\u53d6\u51fa<\/li>\n<li>\u68c0\u67e5\u7269\u54c1\u4e2d\u6709\u6ca1\u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         5<\/p>\n<p>        5<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u53f7\u7269\u54c1&#xff0c;\u6709\u5c31\u5168\u90e8\u53d6\u51fa<\/li>\n<li>\u5982\u679c\u5305\u91cc\u7a7a\u4e86&#xff08;\u5269\u4e0b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         1<\/p>\n<p>        1<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;\u653e\u884c&#xff1b;\u5982\u679c\u8fd8\u6709\u4e1c\u897f&#xff08;\u5269\u4e0b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         &gt;<\/p>\n<p>         1<\/p>\n<p>        &gt;1<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5782em;vertical-align: -0.0391em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;\u62d2\u7edd<\/li>\n<h4>3.2 \u4e07\u80fd\u6a21\u677f \u2014\u2014 \u4f2a\u4ee3\u7801 &#043; \u5b9e\u6218\u4ee3\u7801<\/h4>\n<p>\u4f2a\u4ee3\u7801&#xff1a;<\/p>\n<p>function IsTerminatingNumber(x):<br \/>\n    while x \u80fd\u88ab 2 \u6574\u9664:<br \/>\n        x &#061; x \/ 2<br \/>\n    while x \u80fd\u88ab 5 \u6574\u9664:<br \/>\n        x &#061; x \/ 5<br \/>\n    return x &#061;&#061; 1<\/p>\n<p>\u5b9e\u6218\u4ee3\u7801&#xff08;C&#043;&#043;&#xff09;&#xff1a;<\/p>\n<p><span class=\"token macro property\"><span class=\"token directive-hash\">#<\/span><span class=\"token directive keyword\">include<\/span> <span class=\"token string\">&lt;bits\/stdc&#043;&#043;.h&gt;<\/span><\/span><br \/>\n<span class=\"token keyword\">using<\/span> <span class=\"token keyword\">namespace<\/span> std<span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u68c0\u67e5\u4e00\u4e2a\u6570\u662f\u5426\u53ea\u5305\u542b\u8d28\u56e0\u5b50 2 \u548c 5<\/span><br \/>\n<span class=\"token comment\">\/\/ \u5373&#xff1a;1\/a \u662f\u5426\u80fd\u5316\u4e3a\u6709\u9650\u5c0f\u6570<\/span><br \/>\n<span class=\"token keyword\">bool<\/span> <span class=\"token function\">check<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> x<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token comment\">\/\/ \u6b65\u9aa4\u4e00&#xff1a;\u9664\u5c3d\u6240\u6709\u56e0\u5b50 2<\/span><br \/>\n    <span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span>x <span class=\"token operator\">%<\/span> <span class=\"token number\">2<\/span> <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token punctuation\">{<\/span><br \/>\n        x <span class=\"token operator\">\/&#061;<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u6b65\u9aa4\u4e8c&#xff1a;\u9664\u5c3d\u6240\u6709\u56e0\u5b50 5<\/span><br \/>\n    <span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span>x <span class=\"token operator\">%<\/span> <span class=\"token number\">5<\/span> <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token punctuation\">{<\/span><br \/>\n        x <span class=\"token operator\">\/&#061;<\/span> <span class=\"token number\">5<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u6b65\u9aa4\u4e09&#xff1a;\u5982\u679c\u6700\u7ec8\u7ed3\u679c\u4e3a 1&#xff0c;\u8bf4\u660e x \u53ea\u5305\u542b\u8d28\u56e0\u5b50 2 \u548c 5<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> x <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token keyword\">int<\/span> <span class=\"token function\">main<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> l<span class=\"token punctuation\">,<\/span> r<span class=\"token punctuation\">,<\/span> ans <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    cin <span class=\"token operator\">&gt;&gt;<\/span> l <span class=\"token operator\">&gt;&gt;<\/span> r<span class=\"token punctuation\">;<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u904d\u5386\u533a\u95f4 [l, r]&#xff0c;\u7edf\u8ba1\u7ec8\u6b62\u6570\u4e2a\u6570<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> l<span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> r<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token function\">check<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token punctuation\">{<\/span><br \/>\n            ans<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    cout <span class=\"token operator\">&lt;&lt;<\/span> ans <span class=\"token operator\">&lt;&lt;<\/span> endl<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h4>3.3 \u4f8b\u9898\u5b9e\u73b0 \u2014\u2014 \u672c\u9898\u5b8c\u6574\u4ee3\u7801<\/h4>\n<p>\u4e0a\u9762\u7684\u4ee3\u7801\u5df2\u7ecf\u662f\u672c\u9898\u7684\u5b8c\u6574 AC \u4ee3\u7801\u3002\u6838\u5fc3\u6d41\u7a0b\u53ef\u4ee5\u6982\u62ec\u4e3a&#xff1a;<\/p>\n<li>\u8bfb\u5165\u533a\u95f4 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         [<\/p>\n<p>         L<\/p>\n<p>         ,<\/p>\n<p>         R<\/p>\n<p>         ]<\/p>\n<p>        [L, R]<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u904d\u5386\u533a\u95f4\u4e2d\u7684\u6bcf\u4e2a\u6574\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         i<\/p>\n<p>        i<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6595em\"><\/span><span class=\"mord mathnormal\">i<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u8c03\u7528 check(i) \u5224\u5b9a\u662f\u5426\u4e3a\u7ec8\u6b62\u6570<\/li>\n<li>\u7edf\u8ba1\u6ee1\u8db3\u6761\u4ef6\u7684\u4e2a\u6570\u5e76\u8f93\u51fa<\/li>\n<p>\u4ee5\u6837\u4f8b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        L<\/p>\n<p>        &#061;<\/p>\n<p>        2<\/p>\n<p>        ,<\/p>\n<p>        R<\/p>\n<p>        &#061;<\/p>\n<p>        11<\/p>\n<p>       L&#061;2, R&#061;11<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">11<\/span><\/span><\/span><\/span><\/span> \u4e3a\u4f8b&#xff1a;<\/p>\n<table>\n<tr><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           a<\/p>\n<p>          a<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span>\u9664\u5c3d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           2<\/p>\n<p>          2<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u540e\u9664\u5c3d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           5<\/p>\n<p>          5<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u540e\u5269\u4f59\u662f\u5426\u7ec8\u6b62\u6570<\/tr>\n<tbody>\n<tr>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           2<\/p>\n<p>          2<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           1<\/p>\n<p>          1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           1<\/p>\n<p>          1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           1<\/p>\n<p>          1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u662f<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           3<\/p>\n<p>          3<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           3<\/p>\n<p>          3<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           3<\/p>\n<p>          3<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           3<\/p>\n<p>          3<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u5426<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           4<\/p>\n<p>          4<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">4<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           1<\/p>\n<p>          1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           1<\/p>\n<p>          1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           1<\/p>\n<p>          1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u662f<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           5<\/p>\n<p>          5<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           5<\/p>\n<p>          5<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           1<\/p>\n<p>          1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           1<\/p>\n<p>          1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u662f<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           6<\/p>\n<p>          6<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">6<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           3<\/p>\n<p>          3<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           3<\/p>\n<p>          3<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           3<\/p>\n<p>          3<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u5426<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           7<\/p>\n<p>          7<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           7<\/p>\n<p>          7<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           7<\/p>\n<p>          7<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           7<\/p>\n<p>          7<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u5426<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           8<\/p>\n<p>          8<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">8<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           1<\/p>\n<p>          1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           1<\/p>\n<p>          1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           1<\/p>\n<p>          1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u662f<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           9<\/p>\n<p>          9<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">9<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           9<\/p>\n<p>          9<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">9<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           9<\/p>\n<p>          9<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">9<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           9<\/p>\n<p>          9<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">9<\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u5426<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           10<\/p>\n<p>          10<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">10<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           5<\/p>\n<p>          5<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           1<\/p>\n<p>          1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           1<\/p>\n<p>          1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u662f<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           11<\/p>\n<p>          11<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">11<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           11<\/p>\n<p>          11<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">11<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           11<\/p>\n<p>          11<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">11<\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           11<\/p>\n<p>          11<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">11<\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u5426<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u7ec8\u6b62\u6570\u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>        ,<\/p>\n<p>        4<\/p>\n<p>        ,<\/p>\n<p>        5<\/p>\n<p>        ,<\/p>\n<p>        8<\/p>\n<p>        ,<\/p>\n<p>        10<\/p>\n<p>       2, 4, 5, 8, 10<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8389em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">4<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">5<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">8<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">10<\/span><\/span><\/span><\/span><\/span> \u5171 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        5<\/p>\n<p>       5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u4e2a&#xff0c;\u4e0e\u6837\u4f8b\u8f93\u51fa\u4e00\u81f4\u3002<\/p>\n<h4>3.4 \u5bf9\u6bd4\u5b9e\u73b0 \u2014\u2014 \u5b8c\u6574\u8d28\u56e0\u6570\u5206\u89e3\u53ef\u884c\u5417&#xff1f;<\/h4>\n<p>\u7406\u8bba\u4e0a&#xff0c;\u6211\u4eec\u4e5f\u53ef\u4ee5\u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u505a\u5b8c\u6574\u7684\u8d28\u56e0\u6570\u5206\u89e3&#xff0c;\u7136\u540e\u68c0\u67e5\u5206\u89e3\u7ed3\u679c\u4e2d\u662f\u5426\u53ea\u542b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>       2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        5<\/p>\n<p>       5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>\u3002\u4f46\u56e0\u5b50\u5265\u79bb\u6cd5\u6709\u660e\u663e\u4f18\u52bf&#xff1a;<\/p>\n<table>\n<tr>\u5bf9\u6bd4\u7ef4\u5ea6\u56e0\u5b50\u5265\u79bb\u6cd5\u5b8c\u6574\u8d28\u56e0\u6570\u5206\u89e3<\/tr>\n<tbody>\n<tr>\n<td>\u65f6\u95f4\u590d\u6742\u5ea6<\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           O<\/p>\n<p>           (<\/p>\n<p>           log<\/p>\n<p>           \u2061<\/p>\n<p>           a<\/p>\n<p>           )<\/p>\n<p>          O(\\\\log a)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mop\">lo<span style=\"margin-right: 0.0139em\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff08;\u53ea\u9664 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           2<\/p>\n<p>          2<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           5<\/p>\n<p>          5<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>&#xff09;<\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           O<\/p>\n<p>           (<\/p>\n<p>            a<\/p>\n<p>           )<\/p>\n<p>          O(\\\\sqrt{a})<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0503em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8003em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal\">a<\/span><\/span><\/span><span class=\"\" style=\"top: -2.7603em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>              <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2397em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff08;\u9700\u8981\u8bd5\u9664\u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            a<\/p>\n<p>          \\\\sqrt{a}<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.04em;vertical-align: -0.2397em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8003em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal\">a<\/span><\/span><\/span><span class=\"\" style=\"top: -2.7603em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>              <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2397em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff09;<\/td>\n<\/tr>\n<tr>\n<td>\u4ee3\u7801\u590d\u6742\u5ea6<\/td>\n<td>\u6781\u7b80\u5355&#xff08;\u4e24\u4e2a while \u5faa\u73af&#xff09;<\/td>\n<td>\u8f83\u590d\u6742&#xff08;\u9700\u8981\u8bd5\u9664\u8868\u6216\u7b5b\u6cd5&#xff09;<\/td>\n<\/tr>\n<tr>\n<td>\u9002\u7528\u8303\u56f4<\/td>\n<td>\u4ec5\u5224\u5b9a&#034;\u662f\u5426\u53ea\u542b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           2<\/p>\n<p>          2<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           5<\/p>\n<p>          5<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>&#034;<\/td>\n<td>\u9700\u8981\u5b8c\u6574\u5206\u89e3\u65f6<\/td>\n<\/tr>\n<tr>\n<td>\u5e38\u6570\u56e0\u5b50<\/td>\n<td>\u6781\u5c0f<\/td>\n<td>\u8f83\u5927<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u56e0\u6b64&#xff0c;\u5bf9\u4e8e&#034;\u6709\u9650\u5c0f\u6570\u5224\u5b9a&#034;\u8fd9\u7c7b\u53ea\u9700\u8981\u786e\u8ba4\u7279\u5b9a\u8d28\u56e0\u5b50\u7684\u95ee\u9898&#xff0c;\u56e0\u5b50\u5265\u79bb\u6cd5\u662f\u66f4\u4f18\u9009\u62e9\u3002<\/p>\n<h4>3.5 \u53d8\u4f53\u6e05\u5355 \u2014\u2014 \u8fd9\u7c7b\u95ee\u9898\u7684\u5e38\u89c1\u53d8\u5f62<\/h4>\n<table>\n<tr>\u53d8\u4f53\u7c7b\u578b\u7279\u5f81\u63cf\u8ff0\u5904\u7406\u601d\u8def<\/tr>\n<tbody>\n<tr>\n<td>\u5176\u4ed6\u8fdb\u5236\u4e0b\u7684\u6709\u9650\u5c0f\u6570<\/td>\n<td>\u6bd4\u5982\u4e8c\u8fdb\u5236\u3001\u516b\u8fdb\u5236<\/td>\n<td>\u5c06 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           2<\/p>\n<p>          2<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           5<\/p>\n<p>          5<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u66ff\u6362\u4e3a\u8be5\u8fdb\u5236\u7684\u8d28\u56e0\u5b50&#xff08;\u5982\u4e8c\u8fdb\u5236\u53ea\u542b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           2<\/p>\n<p>          2<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span>&#xff09;<\/td>\n<\/tr>\n<tr>\n<td>\u5206\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            p<\/p>\n<p>            q<\/p>\n<p>          \\\\frac{p}{q}<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.2286em;vertical-align: -0.4811em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7475em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.4461em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">p<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4811em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5224\u5b9a&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           p<\/p>\n<p>           \u2260<\/p>\n<p>           1<\/p>\n<p>          p \\\\neq 1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\"><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"inner\"><span class=\"mord\"><span class=\"mrel\">\ue020<\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace nobreak\"><\/span><span class=\"mrel\">&#061;<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff09;<\/td>\n<td>\u9700\u8981\u5148\u5c06\u5206\u6570\u5316\u4e3a\u6700\u7b80\u5f62\u5f0f<\/td>\n<td>\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           gcd<\/p>\n<p>           \u2061<\/p>\n<p>           (<\/p>\n<p>           p<\/p>\n<p>           ,<\/p>\n<p>           q<\/p>\n<p>           )<\/p>\n<p>          \\\\gcd(p, q)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mop\"><span style=\"margin-right: 0.0139em\">g<\/span>cd<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u7ea6\u5206\u540e&#xff0c;\u518d\u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           q<\/p>\n<p>          q<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span> \u505a\u56e0\u5b50\u5265\u79bb<\/td>\n<\/tr>\n<tr>\n<td>\u7edf\u8ba1 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           [<\/p>\n<p>           1<\/p>\n<p>           ,<\/p>\n<p>           N<\/p>\n<p>           ]<\/p>\n<p>          [1, N]<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span> \u4e2d\u7ec8\u6b62\u6570\u4e2a\u6570<\/td>\n<td>\u8303\u56f4\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           1<\/p>\n<p>          1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u5f00\u59cb<\/td>\n<td>\u76f4\u63a5\u904d\u5386&#xff0c;\u6216\u9884\u5904\u7406\u6807\u8bb0<\/td>\n<\/tr>\n<tr>\n<td>\u6c42\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           k<\/p>\n<p>          k<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span> \u4e2a\u7ec8\u6b62\u6570<\/td>\n<td>\u9700\u8981\u6309\u5e8f\u751f\u6210<\/td>\n<td>\u7528\u4f18\u5148\u961f\u5217\u751f\u6210 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            2<\/p>\n<p>            i<\/p>\n<p>           \u00d7<\/p>\n<p>            5<\/p>\n<p>            j<\/p>\n<p>          2^i \\\\times 5^j<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.908em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8247em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8247em\"><\/span><span class=\"mord\"><span class=\"mord\">5<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8247em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5e8f\u5217<\/td>\n<\/tr>\n<tr>\n<td>\u7ec8\u6b62\u6570\u7684\u4e58\u79ef\/\u548c<\/td>\n<td>\u9700\u8981\u5bf9\u7ec8\u6b62\u6570\u505a\u8fd0\u7b97<\/td>\n<td>\u5229\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            2<\/p>\n<p>            i<\/p>\n<p>           \u00d7<\/p>\n<p>            5<\/p>\n<p>            j<\/p>\n<p>          2^i \\\\times 5^j<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.908em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8247em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8247em\"><\/span><span class=\"mord\"><span class=\"mord\">5<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8247em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u7ed3\u6784\u6027\u8d28<\/td>\n<\/tr>\n<tr>\n<td>\u591a\u7ec4\u8be2\u95ee<\/td>\n<td>\u591a\u6b21\u67e5\u8be2\u4e0d\u540c\u533a\u95f4<\/td>\n<td>\u9884\u5904\u7406\u524d\u7f00\u548c\u6570\u7ec4&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           O<\/p>\n<p>           (<\/p>\n<p>           1<\/p>\n<p>           )<\/p>\n<p>          O(1)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u56de\u7b54\u6bcf\u6b21\u8be2\u95ee<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4>3.6 \u4ec0\u4e48\u65f6\u5019\u4e0d\u80fd\u7528&#xff1f;\u2014\u2014 \u8fb9\u754c\u6761\u4ef6\u548c\u53cd\u4f8b<\/h4>\n<p>\u8fd9\u4e2a\u6a21\u677f\u867d\u7136\u597d\u7528&#xff0c;\u4f46\u4e5f\u6709\u660e\u786e\u7684\u9002\u7528\u8303\u56f4&#xff1a;<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          a<\/p>\n<p>          &#061;<\/p>\n<p>          0<\/p>\n<p>         a &#061; 0<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> \u65e0\u610f\u4e49&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          1<\/p>\n<p>          0<\/p>\n<p>        \\\\frac{1}{0}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span> \u672a\u5b9a\u4e49&#xff0c;\u9898\u76ee\u4fdd\u8bc1 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         L<\/p>\n<p>         \u2265<\/p>\n<p>         1<\/p>\n<p>        L \\\\geq 1<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8193em;vertical-align: -0.136em\"><\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          a<\/p>\n<p>          &#061;<\/p>\n<p>          1<\/p>\n<p>         a &#061; 1<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u662f\u7ec8\u6b62\u6570&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         1<\/p>\n<p>         &#061;<\/p>\n<p>          2<\/p>\n<p>          0<\/p>\n<p>         \u00d7<\/p>\n<p>          5<\/p>\n<p>          0<\/p>\n<p>        1 &#061; 2^0 \\\\times 5^0<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8974em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord\">5<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          1<\/p>\n<p>          1<\/p>\n<p>         &#061;<\/p>\n<p>         1.0<\/p>\n<p>        \\\\frac{1}{1} &#061; 1.0<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1.0<\/span><\/span><\/span><\/span><\/span> \u662f\u6709\u9650\u5c0f\u6570<\/li>\n<li>\u8d1f\u6570\u5904\u7406&#xff1a;\u5982\u679c\u533a\u95f4\u5305\u542b\u8d1f\u6570&#xff0c;\u9700\u8981\u53d6\u7edd\u5bf9\u503c\u540e\u518d\u5224\u5b9a<\/li>\n<li>\u975e\u6700\u7b80\u5206\u6570&#xff1a;\u5982\u679c\u5224\u5b9a\u7684\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          p<\/p>\n<p>          q<\/p>\n<p>        \\\\frac{p}{q}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.2286em;vertical-align: -0.4811em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7475em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.4461em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">p<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4811em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span> \u800c\u975e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          1<\/p>\n<p>          a<\/p>\n<p>        \\\\frac{1}{a}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">a<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5fc5\u987b\u5148\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         gcd<\/p>\n<p>         \u2061<\/p>\n<p>         (<\/p>\n<p>         p<\/p>\n<p>         ,<\/p>\n<p>         q<\/p>\n<p>         )<\/p>\n<p>        \\\\gcd(p, q)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mop\"><span style=\"margin-right: 0.0139em\">g<\/span>cd<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u7ea6\u5206&#xff0c;\u518d\u5bf9\u5206\u6bcd\u505a\u56e0\u5b50\u5265\u79bb\u3002\u4f8b\u5982 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          2<\/p>\n<p>          6<\/p>\n<p>        \\\\frac{2}{6}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">6<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span> \u7ea6\u5206\u540e\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          1<\/p>\n<p>          3<\/p>\n<p>        \\\\frac{1}{3}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5206\u6bcd\u542b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         3<\/p>\n<p>        3<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u662f\u65e0\u9650\u5faa\u73af\u5c0f\u6570<\/li>\n<li>\u5927\u6570\u8303\u56f4&#xff1a;\u5982\u679c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         R<\/p>\n<p>         \u2212<\/p>\n<p>         L<\/p>\n<p>        R &#8211; L<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><\/span> \u5f88\u5927&#xff08;\u5982 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          10<\/p>\n<p>          12<\/p>\n<p>        10^{12}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">12<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;\u9700\u8981\u9884\u5904\u7406\u6216\u6570\u5b66\u65b9\u6cd5\u4f18\u5316&#xff0c;\u4e0d\u80fd\u76f4\u63a5\u904d\u5386<\/li>\n<\/ul>\n<h3>\u56db\u3001\u5e95\u5c42\u903b\u8f91&#xff1a;\u4e3a\u4ec0\u4e48\u8fd9\u4e2a\u7b97\u6cd5\u662f\u5bf9\u7684&#xff1f;<\/h3>\n<h4>4.1 \u5341\u8fdb\u5236\u7684\u57fa\u56e0\u5bc6\u7801<\/h4>\n<p>\u6709\u9650\u5c0f\u6570\u5224\u5b9a\u5b9a\u7406\u7684\u6df1\u5c42\u539f\u56e0&#xff0c;\u5728\u4e8e\u5341\u8fdb\u5236\u7684\u6784\u9020\u65b9\u5f0f\u3002\u5341\u8fdb\u5236\u7684\u6bcf\u4e00\u4f4d\u4ee3\u8868 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        10<\/p>\n<p>       10<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">10<\/span><\/span><\/span><\/span><\/span> \u7684\u5e42\u6b21&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         0.<\/p>\n<p>         a<\/p>\n<p>         b<\/p>\n<p>         c<\/p>\n<p>         &#061;<\/p>\n<p>          a<\/p>\n<p>          10<\/p>\n<p>         &#043;<\/p>\n<p>          b<\/p>\n<p>          100<\/p>\n<p>         &#043;<\/p>\n<p>          c<\/p>\n<p>          1000<\/p>\n<p>         &#061;<\/p>\n<p>           100<\/p>\n<p>           a<\/p>\n<p>           &#043;<\/p>\n<p>           10<\/p>\n<p>           b<\/p>\n<p>           &#043;<\/p>\n<p>           c<\/p>\n<p>          1000<\/p>\n<p>         0.abc &#061; \\\\frac{a}{10} &#043; \\\\frac{b}{100} &#043; \\\\frac{c}{1000} &#061; \\\\frac{100a &#043; 10b &#043; c}{1000} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord\">0.<\/span><span class=\"mord mathnormal\">ab<\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.7936em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.1076em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">10<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0574em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">100<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.7936em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.1076em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1000<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0574em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1000<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">100<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\">10<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u6240\u4ee5\u4efb\u4f55\u6709\u9650\u5c0f\u6570\u90fd\u53ef\u4ee5\u5199\u6210 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         k<\/p>\n<p>          10<\/p>\n<p>          n<\/p>\n<p>       \\\\frac{k}{10^n}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.2251em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8801em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5935em\"><span class=\"\" style=\"top: -2.786em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5f62\u5f0f\u3002\u5f53\u6211\u4eec\u628a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         1<\/p>\n<p>         a<\/p>\n<p>       \\\\frac{1}{a}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">a<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span> \u901a\u5206\u6210\u8fd9\u79cd\u5f62\u5f0f\u65f6&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          1<\/p>\n<p>          a<\/p>\n<p>         &#061;<\/p>\n<p>          k<\/p>\n<p>           10<\/p>\n<p>           n<\/p>\n<p>         \u21d2<\/p>\n<p>         a<\/p>\n<p>         \u22c5<\/p>\n<p>         k<\/p>\n<p>         &#061;<\/p>\n<p>          10<\/p>\n<p>          n<\/p>\n<p>         &#061;<\/p>\n<p>          2<\/p>\n<p>          n<\/p>\n<p>         \u00d7<\/p>\n<p>          5<\/p>\n<p>          n<\/p>\n<p>         \\\\frac{1}{a} &#061; \\\\frac{k}{10^n} \\\\Rightarrow a \\\\cdot k &#061; 10^n &#061; 2^n \\\\times 5^n <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 2.0074em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0574em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5904em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u21d2<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4445em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7144em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7144em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7977em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7144em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7144em\"><\/span><span class=\"mord\"><span class=\"mord\">5<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7144em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u8fd9\u610f\u5473\u7740 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u5fc5\u987b\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         2<\/p>\n<p>         n<\/p>\n<p>        \u00d7<\/p>\n<p>         5<\/p>\n<p>         n<\/p>\n<p>       2^n \\\\times 5^n<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7477em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6644em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6644em\"><\/span><span class=\"mord\"><span class=\"mord\">5<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6644em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u7ea6\u6570&#xff0c;\u56e0\u6b64 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u7684\u8d28\u56e0\u5b50\u53ea\u80fd\u542b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>       2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        5<\/p>\n<p>       5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<h4>4.2 \u56e0\u5b50\u5265\u79bb\u7684\u5b8c\u5907\u6027<\/h4>\n<p>\u4e3a\u4ec0\u4e48&#034;\u9664\u5c3d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>       2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        5<\/p>\n<p>       5<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u540e\u68c0\u67e5\u662f\u5426\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>       1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#034;\u662f\u5b8c\u5907\u7684&#xff1f;\u56e0\u4e3a&#xff1a;<\/p>\n<ul>\n<li>\u5982\u679c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          a<\/p>\n<p>         a<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u53ea\u542b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          2<\/p>\n<p>         2<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          5<\/p>\n<p>         5<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u9664\u5c3d\u540e\u5fc5\u7136\u5269\u4e0b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         1<\/p>\n<p>        1<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u5982\u679c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          a<\/p>\n<p>         a<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u542b\u6709\u5176\u4ed6\u8d28\u56e0\u5b50&#xff1a;\u6bd4\u5982 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         3<\/p>\n<p>        3<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u7531\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         3<\/p>\n<p>        3<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span> \u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         2<\/p>\n<p>        2<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         5<\/p>\n<p>        5<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u90fd\u4e92\u8d28&#xff0c;\u9664 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         2<\/p>\n<p>        2<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         5<\/p>\n<p>        5<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u7684\u8fc7\u7a0b\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         3<\/p>\n<p>        3<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span> \u4e0d\u4f1a\u88ab\u9664\u6389&#xff0c;\u6700\u7ec8\u5269\u4f59\u5927\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         1<\/p>\n<p>        1<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u4e0d\u5b58\u5728\u9057\u6f0f&#xff1a;\u4efb\u4f55\u6b63\u6574\u6570\u7684\u8d28\u56e0\u6570\u5206\u89e3\u662f\u552f\u4e00\u7684&#xff08;\u7b97\u672f\u57fa\u672c\u5b9a\u7406&#xff09;&#xff0c;\u6240\u4ee5\u4e0d\u5b58\u5728&#034;\u5077\u5077\u85cf\u4e86\u5176\u4ed6\u8d28\u56e0\u5b50\u4f46\u6ca1\u88ab\u53d1\u73b0&#034;\u7684\u60c5\u51b5<\/li>\n<\/ul>\n<h4>4.3 \u4ece\u5b9a\u7406\u5230\u4ee3\u7801\u7684\u8f6c\u5316<\/h4>\n<p>\u8fd9\u9053\u9898\u6700\u7cbe\u5f69\u7684\u5730\u65b9&#xff0c;\u4e0d\u662f\u5b9a\u7406\u672c\u8eab&#xff0c;\u800c\u662f\u5982\u4f55\u628a\u62bd\u8c61\u7684\u6570\u8bba\u5b9a\u7406\u8f6c\u5316\u4e3a\u7b80\u6d01\u7684\u4ee3\u7801\u3002\u5b8c\u6574\u7684\u8d28\u56e0\u6570\u5206\u89e3\u9700\u8981\u8bd5\u9664\u6cd5\u6216\u7b5b\u6cd5&#xff0c;\u4f46\u56e0\u5b50\u5265\u79bb\u6cd5\u5229\u7528\u4e86&#034;\u6211\u4eec\u53ea\u9700\u8981\u786e\u8ba4\u6ca1\u6709\u975e\u6cd5\u8d28\u56e0\u5b50&#034;\u8fd9\u4e00\u89c2\u5bdf&#xff0c;\u628a\u590d\u6742\u5ea6\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        O<\/p>\n<p>        (<\/p>\n<p>         a<\/p>\n<p>        )<\/p>\n<p>       O(\\\\sqrt{a})<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0503em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8003em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal\">a<\/span><\/span><\/span><span class=\"\" style=\"top: -2.7603em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>           <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2397em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u964d\u5230\u4e86 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        O<\/p>\n<p>        (<\/p>\n<p>        log<\/p>\n<p>        \u2061<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>       O(\\\\log a)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mop\">lo<span style=\"margin-right: 0.0139em\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002\u8fd9\u63d0\u9192\u6211\u4eec&#xff1a;\u5728\u7ade\u8d5b\u4e2d&#xff0c;&#034;\u5b8c\u6574\u4fe1\u606f&#034;\u5f80\u5f80\u4e0d\u662f\u5fc5\u987b\u7684&#xff0c;&#034;\u8db3\u591f\u505a\u5224\u5b9a&#034;\u7684\u4fe1\u606f\u5f80\u5f80\u53ef\u4ee5\u7528\u66f4\u7b80\u5355\u7684\u65b9\u5f0f\u83b7\u53d6\u3002<\/p>\n<h3>\u4e94\u3001\u51b3\u7b56\u8868&#xff1a;\u9047\u5230\u8fd9\u7c7b\u95ee\u9898\u600e\u4e48\u9009\u7b97\u6cd5&#xff1f;<\/h3>\n<table>\n<tr>\u573a\u666f\u7279\u5f81\u63a8\u8350\u65b9\u6848\u539f\u56e0<\/tr>\n<tbody>\n<tr>\n<td>\u5224\u5b9a\u5355\u4e2a\u6570\u662f\u5426\u4e3a\u7ec8\u6b62\u6570<\/td>\n<td>\u56e0\u5b50\u5265\u79bb\u6cd5&#xff08;\u4e24\u4e2a while&#xff09;<\/td>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           O<\/p>\n<p>           (<\/p>\n<p>           log<\/p>\n<p>           \u2061<\/p>\n<p>           a<\/p>\n<p>           )<\/p>\n<p>          O(\\\\log a)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mop\">lo<span style=\"margin-right: 0.0139em\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4ee3\u7801\u6781\u7b80<\/td>\n<\/tr>\n<tr>\n<td>\u9700\u8981\u5b8c\u6574\u8d28\u56e0\u6570\u5206\u89e3<\/td>\n<td>\u8bd5\u9664\u6cd5 \/ \u7ebf\u6027\u7b5b<\/td>\n<td>\u9700\u8981\u6240\u6709\u8d28\u56e0\u5b50\u53ca\u5176\u6b21\u6570<\/td>\n<\/tr>\n<tr>\n<td>\u8303\u56f4\u6781\u5927&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           R<\/p>\n<p>           \u2265<\/p>\n<p>            10<\/p>\n<p>            12<\/p>\n<p>          R \\\\geq 10^{12}<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8193em;vertical-align: -0.136em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">12<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff09;\u4e14\u591a\u7ec4\u8be2\u95ee<\/td>\n<td>\u9884\u5904\u7406 &#043; \u524d\u7f00\u548c \/ \u6570\u5b66\u516c\u5f0f<\/td>\n<td>\u907f\u514d\u91cd\u590d\u904d\u5386<\/td>\n<\/tr>\n<tr>\n<td>\u5206\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            p<\/p>\n<p>            q<\/p>\n<p>          \\\\frac{p}{q}<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.2286em;vertical-align: -0.4811em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7475em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.4461em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">p<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4811em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5224\u5b9a<\/td>\n<td>\u5148 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           gcd<\/p>\n<p>           \u2061<\/p>\n<p>          \\\\gcd<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mop\"><span style=\"margin-right: 0.0139em\">g<\/span>cd<\/span><\/span><\/span><\/span><\/span> \u7ea6\u5206&#xff0c;\u518d\u56e0\u5b50\u5265\u79bb<\/td>\n<td>\u5fc5\u987b\u5316\u4e3a\u6700\u7b80\u5f62\u5f0f<\/td>\n<\/tr>\n<tr>\n<td>\u5176\u4ed6\u8fdb\u5236&#xff08;\u5982\u4e8c\u8fdb\u5236&#xff09;<\/td>\n<td>\u66ff\u6362\u4e3a\u5bf9\u5e94\u8fdb\u5236\u7684\u8d28\u56e0\u5b50<\/td>\n<td>\u4e8c\u8fdb\u5236\u53ea\u542b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           2<\/p>\n<p>          2<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u516b\u8fdb\u5236\u53ea\u542b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           2<\/p>\n<p>          2<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td>\u6c42\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           k<\/p>\n<p>          k<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span> \u4e2a\u7ec8\u6b62\u6570<\/td>\n<td>\u4f18\u5148\u961f\u5217\u751f\u6210 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            2<\/p>\n<p>            i<\/p>\n<p>           \u00d7<\/p>\n<p>            5<\/p>\n<p>            j<\/p>\n<p>          2^i \\\\times 5^j<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.908em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8247em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8247em\"><\/span><span class=\"mord\"><span class=\"mord\">5<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8247em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<td>\u6309\u5e8f\u751f\u6210&#xff0c;\u907f\u514d\u904d\u5386<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>\u516d\u3001\u5de5\u7a0b\u89c6\u89d2&#xff1a;\u8fd9\u4e2a\u601d\u60f3\u5728\u5b9e\u9645\u4e2d\u6709\u4ec0\u4e48\u7528&#xff1f;<\/h3>\n<p>\u8fd9\u9053\u9898\u867d\u7136\u662f GESP \u4e94\u7ea7\u7684\u57fa\u7840\u9898&#xff0c;\u4f46\u5176\u6838\u5fc3\u601d\u60f3\u5728\u5de5\u7a0b\u4e2d\u6709\u5e7f\u6cdb\u5e94\u7528&#xff1a;<\/p>\n<li>\n<p>\u6d6e\u70b9\u6570\u7cbe\u5ea6\u63a7\u5236&#xff1a;\u5728\u8ba1\u7b97\u673a\u4e2d&#xff0c;\u6d6e\u70b9\u6570\u7684\u8868\u793a\u57fa\u4e8e\u4e8c\u8fdb\u5236&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          2<\/p>\n<p>         2<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u7684\u5e42\u6b21&#xff09;\u3002\u4e00\u4e2a\u5341\u8fdb\u5236\u6709\u9650\u5c0f\u6570\u5728\u4e8c\u8fdb\u5236\u4e0b\u53ef\u80fd\u662f\u65e0\u9650\u5faa\u73af\u7684&#xff08;\u6bd4\u5982 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           0.1<\/p>\n<p>           10<\/p>\n<p>          &#061;<\/p>\n<p>          0.0001100110011<\/p>\n<p>           \u2026<\/p>\n<p>           2<\/p>\n<p>         0.1_{10} &#061; 0.0001100110011\\\\ldots_2<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7944em;vertical-align: -0.15em\"><\/span><span class=\"mord\">0.<\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">10<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7944em;vertical-align: -0.15em\"><\/span><span class=\"mord\">0.0001100110011<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"minner\">\u2026<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;\u8fd9\u4f1a\u5bfc\u81f4\u7cbe\u5ea6\u8bef\u5dee\u3002\u7406\u89e3&#034;\u6709\u9650\u5c0f\u6570\u7684\u8d28\u56e0\u5b50\u5224\u5b9a&#034;\u6709\u52a9\u4e8e\u7a0b\u5e8f\u5458\u9884\u5224\u54ea\u4e9b\u5341\u8fdb\u5236\u5c0f\u6570\u5728\u8ba1\u7b97\u673a\u4e2d\u4f1a\u88ab\u7cbe\u786e\u8868\u793a&#xff0c;\u54ea\u4e9b\u4f1a\u4e22\u5931\u7cbe\u5ea6\u3002<\/p>\n<\/li>\n<li>\n<p>\u91d1\u878d\u7cfb\u7edf\u4e2d\u7684\u91d1\u989d\u8ba1\u7b97&#xff1a;\u94f6\u884c\u7cfb\u7edf\u4e2d\u7ecf\u5e38\u9700\u8981\u5904\u7406&#034;\u7cbe\u786e\u5230\u5206&#034;\u7684\u91d1\u989d\u3002\u7531\u4e8e\u5206\u6bcd\u901a\u5e38\u53ea\u6d89\u53ca <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          2<\/p>\n<p>         2<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          5<\/p>\n<p>         5<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>&#xff08;\u5982 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          0.25<\/p>\n<p>         0.25<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.25<\/span><\/span><\/span><\/span><\/span> \u5143\u3001<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          0.5<\/p>\n<p>         0.5<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.5<\/span><\/span><\/span><\/span><\/span> \u5143\u3001<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          0.125<\/p>\n<p>         0.125<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.125<\/span><\/span><\/span><\/span><\/span> \u5143\u7b49&#xff09;&#xff0c;\u8fd9\u4e9b\u91d1\u989d\u5728\u5341\u8fdb\u5236\u4e0b\u90fd\u662f\u6709\u9650\u5c0f\u6570&#xff0c;\u53ef\u4ee5\u7528\u6574\u6570\u5206&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          1<\/p>\n<p>         1<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u5143 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          &#061;<\/p>\n<p>          100<\/p>\n<p>         &#061; 100<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.3669em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">100<\/span><\/span><\/span><\/span><\/span> \u5206&#xff09;\u7cbe\u786e\u8868\u793a\u3002\u7406\u89e3\u8fd9\u4e00\u6027\u8d28\u6709\u52a9\u4e8e\u8bbe\u8ba1\u4e0d\u4f1a\u4e22\u5931\u7cbe\u5206\u7684\u91d1\u878d\u8ba1\u7b97\u7cfb\u7edf\u3002<\/p>\n<\/li>\n<li>\n<p>\u91c7\u6837\u7387\u4e0e\u6570\u5b57\u4fe1\u53f7\u5904\u7406&#xff1a;\u5728\u97f3\u9891\/\u89c6\u9891\u5904\u7406\u4e2d&#xff0c;\u91c7\u6837\u7387\u7ecf\u5e38\u8bbe\u8ba1\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          2<\/p>\n<p>         2<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u6216 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          5<\/p>\n<p>         5<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u7684\u5e42\u6b21\u7684\u7ec4\u5408&#xff08;\u5982 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          44100<\/p>\n<p>          &#061;<\/p>\n<p>           2<\/p>\n<p>           2<\/p>\n<p>          \u00d7<\/p>\n<p>           3<\/p>\n<p>           2<\/p>\n<p>          \u00d7<\/p>\n<p>           5<\/p>\n<p>           2<\/p>\n<p>          \u00d7<\/p>\n<p>           7<\/p>\n<p>           2<\/p>\n<p>         44100 &#061; 2^2 \\\\times 3^2 \\\\times 5^2 \\\\times 7^2<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">44100<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8974em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8974em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord\">3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8974em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord\">5<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord\">7<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4f46 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          48000<\/p>\n<p>          &#061;<\/p>\n<p>           2<\/p>\n<p>           7<\/p>\n<p>          \u00d7<\/p>\n<p>          3<\/p>\n<p>          \u00d7<\/p>\n<p>           5<\/p>\n<p>           3<\/p>\n<p>         48000 &#061; 2^7 \\\\times 3 \\\\times 5^3<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">48000<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8974em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">7<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">3<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord\">5<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002\u7406\u89e3\u6709\u9650\u5c0f\u6570\u7684\u8d28\u56e0\u5b50\u7ed3\u6784&#xff0c;\u6709\u52a9\u4e8e\u5de5\u7a0b\u5e08\u8bbe\u8ba1\u4e0d\u4f1a\u5728\u65f6\u95f4\u8f74\u4e0a\u4ea7\u751f\u7d2f\u79ef\u8bef\u5dee\u7684\u91c7\u6837\u7cfb\u7edf\u3002<\/p>\n<\/li>\n<h3>\u4e03\u3001\u5c0f\u7ed3<\/h3>\n<p>\u8fd9\u9053\u9898\u6559\u4f1a\u6211\u4eec\u7684\u6838\u5fc3\u8ba4\u77e5\u53ef\u4ee5\u6982\u62ec\u4e3a\u4e00\u53e5\u8bdd&#xff1a;<\/p>\n<p>\u4e00\u4e2a\u5206\u6570\u80fd\u5426\u5316\u4e3a\u6709\u9650\u5c0f\u6570&#xff0c;\u5b8c\u5168\u7531\u5206\u6bcd\u7684\u8d28\u56e0\u5b50\u51b3\u5b9a\u2014\u2014\u5982\u679c\u5206\u6bcd\u53ea\u542b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          2<\/p>\n<p>         2<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          5<\/p>\n<p>         5<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5b83\u5c31\u662f\u6709\u9650\u5c0f\u6570&#xff1b;\u5426\u5219&#xff0c;\u5b83\u5c31\u662f\u65e0\u9650\u5faa\u73af\u5c0f\u6570\u3002<\/p>\n<p>\u7528\u516c\u5f0f\u5316\u8bed\u8a00\u603b\u7ed3&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          1<\/p>\n<p>          a<\/p>\n<p>         \u00a0\u662f\u6709\u9650\u5c0f\u6570<br \/>\n        \u2005\u200a<\/p>\n<p>         \u27fa<br \/>\n        \u2005\u200a<\/p>\n<p>         a<\/p>\n<p>         &#061;<\/p>\n<p>          2<\/p>\n<p>          x<\/p>\n<p>         \u00d7<\/p>\n<p>          5<\/p>\n<p>          y<\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         ,<\/p>\n<p>         y<\/p>\n<p>         \u2265<\/p>\n<p>         0<\/p>\n<p>         )<\/p>\n<p>         \\\\frac{1}{a} \\\\text{ \u662f\u6709\u9650\u5c0f\u6570} \\\\iff a &#061; 2^x \\\\times 5^y \\\\quad (x, y \\\\geq 0) <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 2.0074em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord text\"><span class=\"mord\">\u00a0<\/span><span class=\"mord cjk_fallback\">\u662f\u6709\u9650\u5c0f\u6570<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u27fa<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7977em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7144em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord\">5<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7144em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">0<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5224\u5b9a\u65b9\u6cd5&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         check<\/p>\n<p>         (<\/p>\n<p>         a<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>          (<\/p>\n<p>           a<\/p>\n<p>             2<\/p>\n<p>               v<\/p>\n<p>               2<\/p>\n<p>              (<\/p>\n<p>              a<\/p>\n<p>              )<\/p>\n<p>            \u22c5<\/p>\n<p>             5<\/p>\n<p>               v<\/p>\n<p>               5<\/p>\n<p>              (<\/p>\n<p>              a<\/p>\n<p>              )<\/p>\n<p>          &#061;<\/p>\n<p>          1<\/p>\n<p>          )<\/p>\n<p>         \\\\text{check}(a) &#061; \\\\left( \\\\frac{a}{2^{v_2(a)} \\\\cdot 5^{v_5(a)}} &#061; 1 \\\\right) <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord text\"><span class=\"mord\">check<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.854em;vertical-align: -0.704em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">(<\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.1076em\"><span class=\"\" style=\"top: -2.296em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3173em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0359em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">a<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord\">5<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3173em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0359em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">5<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">a<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.704em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         v<\/p>\n<p>         p<\/p>\n<p>        (<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>       v_p(a)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">p<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u8d28\u56e0\u5b50 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        p<\/p>\n<p>       p<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/span> \u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> 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content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u4ece\u4e00\u9053GESP\u771f\u9898\u51fa\u53d1\uff1a\u804a\u804a\u6709\u9650\u5c0f\u6570\u7684\u8d28\u56e0\u5b50\u5224\u5b9a\u5b9a\u7406 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u9898\u6e90&#xff1a;\u6d1b\u8c37 P15798 [GESP202603 \u4e94\u7ea7] \u6709\u9650\u4e0d\u5faa\u73af\u5c0f\u6570 \u5c0f\u65f6\u5019\u5b66\u5206\u6570\u7684\u65f6\u5019&#xff0c;\u8001\u5e08\u544a\u8bc9\u6211\u4eec 120.5\\frac{1}{2} 0.521\u200b0.5 \u662f\u6709\u9650\u5c0f\u6570&#xff0c;130.333\u2026\\frac{1}{3} 0.333\\ldots31\u200b0.333\u2026 \u662f\u65e0\u9650\u5faa\u73af\u5c0f\u6570\u3002\u4f46\u4f60\u6709\u6ca1\u6709\u60f3\u8fc7&#xff1a;\u4e3a\u4ec0\u4e48\u504f\u504f\u662f 222 \u548c 555 \u80fd\u8ba9\u5c0f\u6570&quot;\u505c\u4e0b\u6765&quot;&#xff1f;\u5982\u679c\u7ed9\u4f60\u4e00\u4e2a\u8303\u56f4&#xff0c;\u6bd4\u5982\u4ece 222 \u5230 111111\" \/>\n<meta property=\"og:url\" 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