{"id":185,"date":"2011-12-02T22:56:40","date_gmt":"2011-12-02T13:56:40","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=185"},"modified":"2021-09-10T20:56:49","modified_gmt":"2021-09-10T11:56:49","slug":"tok200903","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tok200903\/","title":{"rendered":"\u6771\u5de5\u59272009\uff1a\u7b2c3\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(N\\) \u3092\u6b63\u306e\u6574\u6570\u3068\u3059\u308b.\r\n\\(2N\\) \u4ee5\u4e0b\u306e\u6b63\u306e\u6574\u6570 \\(m\\) , \\(n\\) \u304b\u3089\u306a\u308b\u7d44 \\((m, n)\\) \u3067, \u65b9\u7a0b\u5f0f \\(x^2-nx+m=0\\) \u304c \\(N\\) \u4ee5\u4e0a\u306e\u5b9f\u6570\u89e3\u3092\u3082\u3064\u3088\u3046\u306a\u3082\u306e\u306f\u4f55\u7d44\u3042\u308b\u304b.<\/p>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p>\u6761\u4ef6\u3088\u308a\r\n\\[\r\n1 \\leqq m \\leqq 2N , \\ 1 \\leqq n \\leqq 2N \\quad ... [1]\r\n\\]\r\n\\(f(x) = x^2 -nx +m\\) \u3068\u304a\u304f.\r\n\\[\r\nf(x) =\\left( x -\\dfrac{n}{2} \\right)^2 -\\dfrac{n^2}{4} +m\r\n\\]\r\n[1] \u3088\u308a, \\(0 \\lt \\dfrac{n}{2} \\leqq N\\) \u306a\u306e\u3067, \\(f(x)=0\\) \u304c \\(N\\) \u4ee5\u4e0a\u306e\u5b9f\u6570\u89e3\u3092\u3082\u3064\u6761\u4ef6\u306f\r\n\\[\\begin{align}\r\nf(N) & =N^2 -nN +m \\leqq 0 \\\\\r\n\\text{\u2234} \\quad m & \\leqq Nn -N^2 \\quad ... [2]\r\n\\end{align}\\]\r\n\u3086\u3048\u306b, [1] [2] \u3092\u6e80\u305f\u3059\u9818\u57df\u306b\u542b\u307e\u308c\u308b\u683c\u5b50\u70b9\u306e\u500b\u6570\u3092\u6c42\u3081\u308c\u3070\u3088\u3044.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(N = 1\\) \u306e\u3068\u304d\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/toko_200903_01.png\" alt=\"\" title=\"toko_200903_01\" class=\"aligncenter size-full\" \/>\r\n\u6761\u4ef6\u3092\u6e80\u305f\u3059\u70b9\u306f \\(( 2 , 1 )\\) \u306e\u307f\u3067, \\(1\\) \u500b.<\/p><\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(N \\geqq 2\\) \u306e\u3068\u304d\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/toko_200903_02.png\" alt=\"\" title=\"toko_200903_02\" class=\"aligncenter size-full\" \/>\r\n\u6761\u4ef6\u3092\u6e80\u305f\u3059\u70b9\u306f,\r\n<ul>\r\n<li><p>\\(m = N+1\\) \u4e0a\u306b, \\(N\\) \u500b<\/p><\/li>\r\n<li><p>\\(m = k \\ ( N+2 \\leqq k \\leqq N^2 )\\) \u4e0a\u306b, \\(2N\\) \u500b\u305a\u3064\r\n\u5b58\u5728\u3059\u308b\u306e\u3067\r\n\\[\r\nN +2N (N-1) = 2N^2-N \\ \\text{\u500b}\r\n\\]<\/li>\r\n<\/ul>\r\n\u3053\u308c\u306f \\(N=1\\) \u306e\u3068\u304d\u3082\u6e80\u305f\u3057\u3066\u3044\u308b.<\/p><\/li>\r\n<\/ol>\r\n<p>\u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u7d44\u6570\u306f\r\n\\[\r\n\\underline{2N^2-N}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(N\\) \u3092\u6b63\u306e\u6574\u6570\u3068\u3059\u308b. \\(2N\\) \u4ee5\u4e0b\u306e\u6b63\u306e\u6574\u6570 \\(m\\) , \\(n\\) \u304b\u3089\u306a\u308b\u7d44 \\((m, n)\\) \u3067, \u65b9\u7a0b\u5f0f \\(x^2-nx+m=0\\) \u304c \\(N\\) \u4ee5\u4e0a\u306e\u5b9f\u6570\u89e3\u3092\u3082\u3064\u3088\u3046\u306a\u3082\u306e\u306f\u4f55\u7d44\u3042 &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/tok200903\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/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":[24],"tags":[141,15],"class_list":["post-185","post","type-post","status-publish","format-standard","hentry","category-toko_2009","tag-toko","tag-15"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/185","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=185"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/185\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=185"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=185"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}