{"version":"https://jsonfeed.org/version/1.1","title":"苏迟但到的主页","home_page_url":"https://kexohproject.pages.dev","feed_url":"https://kexohproject.pages.dev/json/","description":"<p>你好，欢迎访问个人主页！</p><p>擅长密码学，安全分析，数字水印等技术。</p><p>你可以联系我通过:findmykexin@gmail.com或者知乎私信。</p><p>我的知乎链接：<a href=\"https://www.zhihu.com/people/su-chi-dan-dao\" rel=\"noopener noreferrer\" target=\"_blank\">苏迟但到 - 知乎 (zhihu.com)</a></p><p>我的github链接：<a href=\"https://github.com/kexinoh\" rel=\"noopener noreferrer\" target=\"_blank\">kexinoh</a></p>","icon":"https://kexohcdn.gptapi.cyou/kexohproject/production/images/channel-2e54d141ee195646ca12a9d16507a908.jpg","favicon":"https://kexohcdn.gptapi.cyou/kexohproject/production/images/favicon-340a2925d02a0386f3b954a032834917.jpg","authors":[{"name":"苏迟但到"}],"language":"zh-cn","items":[{"id":"rKCjQ-WelWa","title":"欧拉函数是否除了素数都可以取到？","content_html":"<p data-pid=\"XBSupf-H\">当然不是。</p><p data-pid=\"-Q_TJy3w\">举一个最简单例子，9.</p><p data-pid=\"QktsXDZY\">你不能找到任意一个数x,使得它的欧拉函数等于9.</p><p data-pid=\"CK9kQKu8\">9=3*3.</p><p data-pid=\"AjZrnB1_\">下面我们来简单证明一下这个数不存在。</p><p data-pid=\"HSQfI-_L\">假设存在一个数x，使得 <img src=\"https://www.zhihu.com/equation?tex=%5Cvarphi%28x%29%3D9\" alt=\"\\varphi(x)=9\" eeimg=\"1\"/> .如果x是2的倍数，那么也一定存在一个数y=x/2，同时也满足 <img src=\"https://www.zhihu.com/equation?tex=%5Cvarphi%28y%29%3D9\" alt=\"\\varphi(y)=9\" eeimg=\"1\"/> .</p><p data-pid=\"Hin0nMoU\">因此不妨设x不含因子2.</p><p data-pid=\"IhRHFI9y\">如果这个数有三个素因子及以上。</p><p data-pid=\"o3hwP8Iu\"><img src=\"https://www.zhihu.com/equation?tex=%5Cvarphi%28x%29%3E%3D2%5Ctimes4%5Ctimes6%3D48\" alt=\"\\varphi(x)&gt;=2\\times4\\times6=48\" eeimg=\"1\"/> </p><p data-pid=\"J3gJ1rP9\">如果只有一个素因子，那么 <img src=\"https://www.zhihu.com/equation?tex=%5Cvarphi%28x%29%3Dx-1%3D9%2Cx%3D10\" alt=\"\\varphi(x)=x-1=9,x=10\" eeimg=\"1\"/> 与只有一个素因子相矛盾。</p><p data-pid=\"vYeMXDDh\">如果有两个素因子，那么可以简单使用排除法，最小的两素因子（不含2）只有3*5，它的 <img src=\"https://www.zhihu.com/equation?tex=%5Cvarphi%2815%29%3D8\" alt=\"\\varphi(15)=8\" eeimg=\"1\"/> .易得其余的均大于12。</p><p data-pid=\"Y-2PNKTc\">因此综上所述，不存在欧拉函数为9的数。</p>","content_text":"当然不是。\n\n举一个最简单例子，9.\n\n你不能找到任意一个数x,使得它的欧拉函数等于9.\n\n9=3*3.\n\n下面我们来简单证明一下这个数不存在。\n\n假设存在一个数x，使得 \\varphi(x)=9\n[https://www.zhihu.com/equation?tex=%5Cvarphi%28x%29%3D9]\n.如果x是2的倍数，那么也一定存在一个数y=x/2，同时也满足 \\varphi(y)=9\n[https://www.zhihu.com/equation?tex=%5Cvarphi%28y%29%3D9] .\n\n因此不妨设x不含因子2.\n\n如果这个数有三个素因子及以上。\n\n\\varphi(x)>=2\\times4\\times6=48\n[https://www.zhihu.com/equation?tex=%5Cvarphi%28x%29%3E%3D2%5Ctimes4%5Ctimes6%3D48]\n\n如果只有一个素因子，那么 \\varphi(x)=x-1=9,x=10\n[https://www.zhihu.com/equation?tex=%5Cvarphi%28x%29%3Dx-1%3D9%2Cx%3D10]\n与只有一个素因子相矛盾。\n\n如果有两个素因子，那么可以简单使用排除法，最小的两素因子（不含2）只有3*5，它的 \\varphi(15)=8\n[https://www.zhihu.com/equation?tex=%5Cvarphi%2815%29%3D8] .易得其余的均大于12。\n\n因此综上所述，不存在欧拉函数为9的数。","date_published":"2022-11-01T03:19:27.000Z","_microfeed":{"web_url":"https://kexohproject.pages.dev/i/欧拉函数是否除了素数都可以取到-rKCjQ-WelWa/","json_url":"https://kexohproject.pages.dev/i/rKCjQ-WelWa/json/","rss_url":"https://kexohproject.pages.dev/i/rKCjQ-WelWa/rss/","guid":"rKCjQ-WelWa","status":"published","itunes:title":"New Article Title for iTunes","date_published_short":"Mon Oct 31 2022","date_published_ms":1667272767000}}],"_microfeed":{"microfeed_version":"0.1.2","base_url":"https://kexohproject.pages.dev","categories":[{"name":"Education","categories":[{"name":"Language Learning"}]},{"name":"Technology"}],"subscribe_methods":[{"name":"RSS","type":"rss","url":"https://kexohproject.pages.dev/rss/","image":"https://kexohproject.pages.dev/assets/brands/subscribe/rss.png","enabled":true,"editable":false,"id":"4KlfbtkEfzy"},{"name":"JSON","type":"json","url":"https://kexohproject.pages.dev/json/","image":"https://kexohproject.pages.dev/assets/brands/subscribe/json.png","enabled":true,"editable":false,"id":"DVFm7TYiNSq"}],"description_text":"你好，欢迎访问个人主页！\n\n擅长密码学，安全分析，数字水印等技术。\n\n你可以联系我通过:findmykexin@gmail.com或者知乎私信。\n\n我的知乎链接：苏迟但到 - 知乎 (zhihu.com)\n\n我的github链接：kexinoh","copyright":"©2024","itunes:type":"episodic","items_sort_order":"newest_first"}}