{"id":612,"date":"2013-02-11T09:51:42","date_gmt":"2013-02-11T00:51:42","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=612"},"modified":"2021-03-24T09:48:13","modified_gmt":"2021-03-24T00:48:13","slug":"kyr200703","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr200703\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb\u4e592007\uff1a\u7b2c3\u554f"},"content":{"rendered":"
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\\(p\\) \u3092 \\(3\\) \u4ee5\u4e0a\u306e\u7d20\u6570\u3068\u3059\u308b. \\(4\\) \u500b\u306e\u6574\u6570 \\(a , b , c , d\\) \u304c\u6b21\u306e \\(3\\) \u6761\u4ef6\r\n\\[\r\na+b+c+d = 0 , \\ ad-bc+p = 0 , \\ a \\geqq b \\geqq c \\geqq d\r\n\\]\r\n\u3092\u6e80\u305f\u3059\u3068\u304d, \\(a , b , c , d\\) \u3092 \\(p\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p>\r\n

\r\n\r\n

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

\\(a+b+c+d = 0\\) \u3088\u308a\r\n\\[\r\nd = -(a+b+c) \\quad ... [1]\r\n\\]\r\n\u3053\u308c\u3092 \\(ad-bc+p = 0\\) \u306b\u4ee3\u5165\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n-a (a+b+c) -bc +p & = 0 \\\\\r\n\\text{\u2234} \\quad (a+b)(a+c) & = p\r\n\\end{align}\\]\r\n\\(a+b \\geqq a+c\\) \u306a\u306e\u3067\r\n\\[\r\n( a+b , a+c ) = (-1 , -p ) , \\, ( p , 1 )\r\n\\]\r\n

    \r\n

  1. 1*<\/strong>\u3000\\(( a+b , a+c ) = ( -1 , -p )\\) \u306e\u3068\u304d\r\n\\[\r\nb = -1-a , \\ c = -p-a\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\r\nd = - ( a -1-a -p-a ) = a+p+1\r\n\\]\r\n\u3057\u304b\u3057, \u3053\u308c\u306f \\(a \\geqq d\\) \u306b\u77db\u76fe\u3059\u308b\u305f\u3081\u4e0d\u9069.<\/p><\/li>\r\n

  2. 2*<\/strong>\u3000\\(( a+b , a+c ) = ( p , 1 )\\) \u306e\u3068\u304d\r\n\\[\r\nb = p-a , \\ c = 1-a \\quad ... [2]\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\r\nd = - ( a +p-a +1-a ) = a-p-1 \\quad ... [3]\r\n\\]\r\n\\(a \\geqq b\\) \u3088\u308a\r\n\\[\\begin{align}\r\na & \\geqq p-a \\\\\r\n\\text{\u2234} \\quad a & \\geqq \\dfrac{p}{2} \\quad ... [4]\r\n\\end{align}\\]\r\n\\(c \\geqq d\\) \u3088\u308a,\r\n\\[\\begin{align}\r\n1-a & \\geqq a-p-1 \\\\\r\n\\text{\u2234} \\quad a & \\leqq \\dfrac{p}{2} +1 \\quad ... [5]\r\n\\end{align}\\]\r\n\\(p\\) \u306f\u5947\u6570, \\(a\\) \u306f\u6574\u6570\u306a\u306e\u3067, [4] [5] \u3088\u308a\r\n\\[\r\na = \\dfrac{p+1}{2}\r\n\\]\r\n[2] [3] \u3088\u308a\r\n\\[\r\nb = \\dfrac{p-1}{2} , \\ c = -\\dfrac{p-1}{2} , \\ d = -\\dfrac{p+1}{2}\r\n\\]<\/li>\r\n<\/ol>\r\n

    1*<\/strong> 2*<\/strong>\u3088\u308a, \u6c42\u3081\u308b\u5024\u306f\r\n\\[\r\n( a , b , c , d ) = \\underline{\\left( \\dfrac{p+1}{2} , \\dfrac{p-1}{2} , -\\dfrac{p-1}{2} , -\\dfrac{p+1}{2} \\right)}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(p\\) \u3092 \\(3\\) \u4ee5\u4e0a\u306e\u7d20\u6570\u3068\u3059\u308b. \\(4\\) \u500b\u306e\u6574\u6570 \\(a , b , c , d\\) \u304c\u6b21\u306e \\(3\\) \u6761\u4ef6 \\[ a+b+c+d = 0 , \\ ad-bc+p = 0 , \\ a \\geqq b … \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":[87],"tags":[140,109],"class_list":["post-612","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2007","tag-kyoto_r","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/612","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=612"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/612\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=612"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=612"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=612"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}