{"author_url":"https://blog.hatena.ne.jp/derwind/","blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6","blog_url":"https://randommemory.hatenablog.com/","published":"2016-09-27 03:10:42","type":"rich","title":"Galois\u7406\u8ad6(57)\u2015\u5186\u5206\u591a\u9805\u5f0f\u306e\u65e2\u7d04\u6027\u3068\u5186\u5206\u62e1\u5927","author_name":"derwind","image_url":null,"description":"Theorem \u5186\u5206\u591a\u9805\u5f0f $\\phi_n$ \u306f $\\Q[X]$ \u3067\u65e2\u7d04\u3067\u3042\u308b\u3002 proof $\\mu_n$ \u306e\u751f\u6210\u5143 $\\zeta$ \u3092\u3068\u308b\u3002 $(p,n)=1$ \u306a\u308b\u7d20\u6570 $p$ \u3092\u3068\u308b\u3068\u3001 $\\zeta^p$ \u3082\u539f\u59cb\u6839\u3067\u3042\u308b\u3002 $\\phi_n = P_\\min(\\zeta,\\Q)\\cdot g,\\ g \\in \\Z[X]$ \u3068\u66f8\u3051\u308b\u3002 $P = P_\\min(\\zeta,\\Q)$ \u3068\u304a\u304f\u3002 $0 = \\phi_n(\\zeta^p) = P(\\zeta^p) g(\\zeta^p)$ \u3088\u308a $P(\\zeta^p) = 0$ \u6216\u306f $g(\\zeta^p) = 0$ \u3067\u3042\u308b\u3002 $P \\neq P\u2026","version":"1.0","width":"100%","provider_url":"https://hatena.blog","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2016%2F09%2F27%2F031042\" title=\"Galois\u7406\u8ad6(57)\u2015\u5186\u5206\u591a\u9805\u5f0f\u306e\u65e2\u7d04\u6027\u3068\u5186\u5206\u62e1\u5927 - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6\" class=\"embed-card embed-blogcard\" scrolling=\"no\" frameborder=\"0\" style=\"display: block; width: 100%; height: 190px; max-width: 500px; margin: 10px 0px;\"></iframe>","provider_name":"Hatena Blog","url":"https://randommemory.hatenablog.com/entry/2016/09/27/031042","height":"190","categories":["math-alg"]}