{"id":360,"date":"2012-04-07T12:29:34","date_gmt":"2012-04-07T03:29:34","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=360"},"modified":"2021-03-10T20:18:38","modified_gmt":"2021-03-10T11:18:38","slug":"tkr201204","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkr201204\/","title":{"rendered":"\u6771\u5927\u7406\u7cfb2012\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\\(n\\) \u3092 \\(2\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b.\r\n\u81ea\u7136\u6570\uff08 \\(1\\) \u4ee5\u4e0a\u306e\u6574\u6570\uff09\u306e \\(n\\) \u4e57\u306b\u306a\u308b\u6570\u3092 \\(n\\) \u4e57\u6570\u3068\u547c\u3076\u3053\u3068\u306b\u3059\u308b. \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u9023\u7d9a\u3059\u308b \\(2\\) \u500b\u306e\u81ea\u7136\u6570\u306e\u7a4d\u306f \\(n\\) \u4e57\u6570\u3067\u306a\u3044\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u9023\u7d9a\u3059\u308b \\(n\\) \u500b\u306e\u81ea\u7136\u6570\u306e\u7a4d\u306f \\(n\\) \u4e57\u6570\u3067\u306a\u3044\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

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

    \\[\r\nm (m+1) =a^n \\quad ... [ \\text{A} ]\r\n\\]\r\n[A] \u3092\u307f\u305f\u3059\u81ea\u7136\u6570 \\(m\\) , \\(a\\) \u304c\u5b58\u5728\u3059\u308b\u3068\u4eee\u5b9a\u3059\u308b.
    \r\n\\(m\\) \u3068 \\(m+1\\) \u306f\u4e92\u3044\u306b\u7d20\u306a\u306e\u3067, \\(a=bc \\quad ( b \\lt c )\\) \u3092\u307f\u305f\u3059\u81ea\u7136\u6570 \\(b\\) , \\(c\\) \u3092\u7528\u3044\u3066\r\n\\[\r\nm =b^n , \\quad m+1 =c^n\r\n\\]\r\n\u3068\u8868\u305b\u308b. \u3053\u306e\u3068\u304d\r\n\\[\r\nc^n -b^n =1\r\n\\]\r\n\u3057\u304b\u3057\r\n\\[\r\nc^n -b^n \\gt 2^2 -1^2 =3\r\n\\]\r\n\u306a\u306e\u3067, [A] \u3092\u307f\u305f\u3059 \\(m\\) \u306f\u5b58\u5728\u305b\u305a, \u77db\u76fe\u3059\u308b.
    \r\n\u3088\u3063\u3066, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n

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

    (1)<\/strong> \u306e\u7d50\u679c\u3088\u308a, \\(n=2\\) \u306e\u3068\u304d\u306f\u793a\u3055\u308c\u3066\u3044\u308b.
    \r\n\\(n \\geqq 3\\) \u306e\u3068\u304d\u306b\u3064\u3044\u3066\u8003\u3048\u308b.\r\n\\[\r\nm (m+1) \\cdots (m+n-1) =a^n \\quad ... [ \\text{B} ]\r\n\\]\r\n[B] \u3092\u307f\u305f\u3059\u81ea\u7136\u6570 \\(m\\) , \\(a\\) \u304c\u5b58\u5728\u3059\u308b\u3068\u4eee\u5b9a\u3059\u308b.
    \r\n[B] \u3088\u308a\r\n\\[\r\nm+1 \\leqq a \\leqq m+n-2\r\n\\]\r\n\u3053\u3053\u3067 \\(a =m+k \\quad (1 \\leqq k \\leqq n-2 )\\) \u3068\u304a\u304f\u3068, [B] \u3088\u308a\r\n\\[\\begin{align}\r\nm \\cdots (m+k-1)(m+k)(m+k+1) \\cdots (m+n-1) & = (m+k)^n \\\\\r\n\\text{\u2234} \\quad m \\cdots (m+k-1)(m+k+1) \\cdots (m+n-1) & = (m+k)^{n-1}\r\n\\end{align}\\]\r\n\u3057\u304b\u3057, \\(m+k\\) \u3068 \\(m+k-1\\) \u306f\u4e92\u3044\u306b\u7d20\u306a\u306e\u3067, \u77db\u76fe\u3059\u308b.
    \r\n\u3088\u3063\u3066, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\\(n\\) \u3092 \\(2\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b. \u81ea\u7136\u6570\uff08 \\(1\\) \u4ee5\u4e0a\u306e\u6574\u6570\uff09\u306e \\(n\\) \u4e57\u306b\u306a\u308b\u6570\u3092 \\(n\\) \u4e57\u6570\u3068\u547c\u3076\u3053\u3068\u306b\u3059\u308b. \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. (1)\u3000\u9023\u7d9a\u3059\u308b \\(2\\) \u500b\u306e\u81ea\u7136\u6570\u306e\u7a4d\u306f \\ … \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":[58],"tags":[139,68],"class_list":["post-360","post","type-post","status-publish","format-standard","hentry","category-tokyo_r_2012","tag-tokyo_r","tag-68"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/360","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=360"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/360\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=360"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=360"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=360"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}