{"id":426,"date":"2023-01-02T15:03:57","date_gmt":"2023-01-02T07:03:57","guid":{"rendered":"https:\/\/blog.cirno.fun\/?p=426"},"modified":"2024-09-12T09:30:04","modified_gmt":"2024-09-12T01:30:04","slug":"%e4%b8%ad%e5%9b%bd%e5%89%a9%e4%bd%99%e5%ae%9a%e7%90%86","status":"publish","type":"post","link":"https:\/\/blog.sssn.tech\/?p=426","title":{"rendered":"\u4e2d\u56fd\u5269\u4f59\u5b9a\u7406"},"content":{"rendered":"<p>\u7b80\u5355\u4ecb\u7ecd\u4e2d\u56fd\u5269\u4f59\u5b9a\u7406 \u5bf9\u4e8e\u540c\u4f59\u65b9\u7a0b\u7ec4\uff1a<\/p>\n<pre><code class=\"language-katex\">\\begin{cases}\n  &amp;  x \\equiv a_1 \\quad (mod \\quad m_1)\\\\\n  &amp;  x \\equiv a_2 \\quad (mod \\quad m_2)\\\\\n  &amp; \\cdot \\cdot \\cdot \\\\\n  &amp; x \\equiv a_i \\quad (mod \\quad m_i)\n\\end{cases}<\/code><\/pre>\n<p>\u89c4\u5b9a\u7ea6\u675f\uff1a<code>m_i<\/code>\u4e4b\u95f4<strong>\u4e24\u4e24\u4e92\u8d28<\/strong>\u5219x\u6709\u516c\u5f0f\u89e3,\u53ea\u9700\u4ee4<\/p>\n<pre><code class=\"language-katex\">M=\\prod  m_i\uff0c M_i=\\frac{M}{m_i}\\\\\nM_i^{-1}\u4e3aM_imod \\quad m_i\u7684\u9006<\/code><\/pre>\n<p>\u5219<\/p>\n<pre><code class=\"language-katex\">x=(\\sum M_i^{-1}M_ia_i )mod \\quad M<\/code><\/pre>\n<p>\u4e00\u4e2a\u7b80\u8981\u7684\u9a8c\u8bc1\uff1a \u5bf9\u4e8ex\u6c42\u548c\u7684\u4efb\u610f\u7b2ci\u9879<\/p>\n<pre><code class=\"language-katex\">M_i^{-1}M_ia_i \\\\ M_i^{-1}\u4e3aM_imod \\quad m_i\u7684\u9006<\/code><\/pre>\n<p>\u5176\u4e2d\u7684\u56e0\u5b50<code>M_i<\/code>\u5305\u542b\u9664<code>m_i<\/code>\u4ee5\u5916\u7684\u6240\u6709m\uff0c\u6240\u4ee5\u9664<code>m_k, k \\ne i<\/code>\u7684\u4f59\u6570\u90fd\u662f\u96f6 \u5e76\u4e14\u7531\u4e58\u6cd5\u9006\u5143\u5b9a\u4e49\u53ef\u77e5\uff0c\u8be5\u9879mod <code>m_i<\/code>\u7684\u4f59\u6570\u662f<code>a_i<\/code><\/p>\n<p>\u5373\uff0cx\u7531i\u9879\u6c42\u548c\u7ec4\u6210\uff0c\u6bcf\u4e00\u9879\u90fd\u5bf9\u65b9\u7a0b\u7ec4\u4e2d\u7b2ci\u4e2a\u65b9\u7a0b\u8d1f\u8d23\uff0c\u800c\u5bf9\u7b2ci\u4e2a\u65b9\u7a0b\u8d1f\u8d23\u65f6\uff0c\u5176\u4ed6\u9879\u90fd\u4e3a0\uff0c\u6545\u516c\u5f0f\u89e3\u6b63\u786e<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7b80\u5355\u4ecb\u7ecd\u4e2d\u56fd\u5269\u4f59\u5b9a\u7406 \u5bf9\u4e8e\u540c\u4f59\u65b9\u7a0b\u7ec4\uff1a \\begin{cases} &amp;  [&#8230;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13,16],"tags":[],"class_list":["post-426","post","type-post","status-publish","format-standard","hentry","category-13","category-16"],"_links":{"self":[{"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts\/426","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=426"}],"version-history":[{"count":1,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts\/426\/revisions"}],"predecessor-version":[{"id":732,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts\/426\/revisions\/732"}],"wp:attachment":[{"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=426"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=426"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=426"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}