{"id":634,"date":"2013-02-15T00:31:47","date_gmt":"2013-02-14T15:31:47","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=634"},"modified":"2021-09-10T21:28:19","modified_gmt":"2021-09-10T12:28:19","slug":"tok200701","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tok200701\/","title":{"rendered":"\u6771\u5de5\u59272007\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\\(p\\) \u3092\u7d20\u6570, \\(n\\) \u3092 \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(m\\) \u306f\u6574\u6570\u3067 \\(0 \\leqq m \\leqq n\\) \u3068\u3059\u308b. \\(1\\) \u304b\u3089 \\(p^{n+1}\\) \u307e\u3067\u306e\u6574\u6570\u306e\u4e2d\u3067, \\(p^m\\) \u3067\u5272\u308a\u5207\u308c \\(p^{m+1}\\) \u3067\u5272\u308a\u5207\u308c\u306a\u3044\u3082\u306e\u306e\u500b\u6570\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(1\\) \u304b\u3089 \\(p^{n+1}\\) \u307e\u3067\u306e \\(2\\) \u3064\u306e\u6574\u6570 \\(x , y\\) \u306b\u5bfe\u3057, \u305d\u306e\u7a4d\u304c \\(p^{n+1}\\) \u3067\u5272\u308a\u5207\u308c\u308b\u3088\u3046\u306a\u7d44 \\((x,y)\\) \u306e\u500b\u6570\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

    (1)<\/strong><\/p>\r\n

    \\(p^{m}\\) \u3067\u5272\u308a\u5207\u308c\u308b\u6574\u6570\u306e\u500b\u6570\u306f\r\n\\[\r\n\\dfrac{p^{n+1}}{p^m} = p^{n-m+1}\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u500b\u6570\u306f\r\n\\[\r\np^{n-m+1} -p^{n-(m+1)+1} =\\underline{p^{n-m}(p-1)}\r\n\\]\r\n

    (2)<\/strong><\/p>\r\n

      \r\n

    1. 1*<\/strong>\u3000\\(x = p^{n+1}\\) \u306e\u3068\u304d
      \r\n\\(y\\) \u306f\u3069\u306e\u6574\u6570\u3067\u3082\u3088\u3044\u306e\u3067, \\((x,y)\\) \u306e\u7d44\u306e\u500b\u6570\u306f\r\n\\[\r\np^{n+1}\r\n\\]<\/li>\r\n

    2. 2*<\/strong>\u3000\\(x\\) \u304c \\(p^{m}\\) \u3067\u5272\u5207\u308c \\(p^{m+1}\\) \u3067\u5272\u5207\u308c\u306a\u3044\uff08 \\(0 \\leqq m \\leqq n\\) \uff09\u3068\u304d
      \r\n\\(y\\) \u304c \\(p^{n-m+1}\\) \u3067\u5272\u5207\u308c\u308c\u3070\u3088\u3044\u306e\u3067, \\((x,y)\\) \u306e\u7d44\u306e\u500b\u6570 \\(K _ m\\) \u306f, (1)<\/strong> \u306e\u7d50\u679c\u3092\u7528\u3044\u3066\r\n\\[\\begin{align}\r\nK _ m & = p^{n-m}(p-1) \\cdot p^{n-(n-m+1)+1} \\\\\r\n& = p^{n}(p-1)\r\n\\end{align}\\]<\/li>\r\n<\/ol>\r\n

      \u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u500b\u6570\u306f\r\n\\[\\begin{align}\r\np^{n+1} +\\textstyle\\sum\\limits _ {m=0}^n K _ m & = p^{n+1} + (n+1)p^{n}(p-1) \\\\\r\n& = p^{n} \\left\\{ p +(n+1)(p-1) \\right\\} \\\\\r\n& =\\underline{p^{n} \\left\\{ (n+2)p -n-1 \\right\\}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\\(p\\) \u3092\u7d20\u6570, \\(n\\) \u3092 \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b. (1)\u3000\\(m\\) \u306f\u6574\u6570\u3067 \\(0 \\leqq m \\leqq n\\) \u3068\u3059\u308b. \\(1\\) \u304b\u3089 \\(p^{n+1}\\) \u307e\u3067\u306e\u6574\u6570\u306e\u4e2d\u3067, \\( … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[91],"tags":[141,109],"class_list":["post-634","post","type-post","status-publish","format-standard","hentry","category-toko_2007","tag-toko","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/634","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=634"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/634\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=634"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=634"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=634"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}