{"id":213,"date":"2011-12-03T00:06:21","date_gmt":"2011-12-02T15:06:21","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=213"},"modified":"2021-11-04T13:11:22","modified_gmt":"2021-11-04T04:11:22","slug":"htb200901","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb200901\/","title":{"rendered":"\u4e00\u6a4b\u59272009\uff1a\u7b2c1\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(2\\) \u4ee5\u4e0a\u306e\u6574\u6570 \\(m , n\\) \u306f \\(m^3+1^3 = n^3+10^3\\) \u3092\u307f\u305f\u3059.\r\n\\(m , n\\) \u3092\u6c42\u3081\u3088.<\/p>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p>\u4e0e\u5f0f\u3088\u308a\r\n\\[\\begin{align}\r\nm^3-n^3 & = 999 \\\\\r\n\\text{\u2234} \\quad (m-n)(m^2+mn+n^2) & = 3^3 \\cdot 37\r\n\\end{align}\\]\r\n\u3053\u3053\u3067,\r\n\\[\r\n0 \\lt m-n \\lt (m-n)^2 \\lt m^2+mn+n^2\r\n\\]\r\n\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3059\u308c\u3070, \u89e3\u306e\u5019\u88dc\u306f\r\n\\[\r\n( m , n ) = (1 , 999) , (3, 333) , (9, 111)\r\n\\]\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(( m , n ) = (1 , 999)\\) \u306e\u3068\u304d\r\n\\(m =n+1\\) \u3092\u4ee3\u5165\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n(n+1)^2 +(n+1)n +n^2 & = 999 \\\\\r\n3n^2 +3n-998 & = 0\r\n\\end{align}\\]\r\n\u3053\u308c\u306f\u6574\u6570\u89e3\u3092\u6301\u305f\u306a\u3044\u306e\u3067, \u4e0d\u9069.<\/p><\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(( m , n ) = (3, 333)\\) \u306e\u3068\u304d\r\n\\(m =n+3\\) \u3092\u4ee3\u5165\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n(n+3)^2 +(n+3)n +n^2 & = 333 \\\\\r\nn^2 +3n-108 & = 0 \\\\\r\n(n-9)(n+12) & = 0 \\\\\r\n\\text{\u2234} \\quad n = 9 , \\ m & = 12\r\n\\end{align}\\]<\/li>\r\n<li><p><strong>3*<\/strong>\u3000\\(( m , n ) = (9, 111)\\) \u306e\u3068\u304d\r\n\\(m =n+9\\) \u3092\u4ee3\u5165\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n(n+9)^2 +(n+9)n +n^2 & = 111 \\\\\r\nn^2 +9n-10 & = 0 \\\\\r\n(n-1)(n+10) & = 0\r\n\\end{align}\\]\r\n\u3053\u308c\u306f \\(n \\geqq 2\\) \u3092\u6e80\u305f\u3055\u306a\u3044\u306e\u3067\u4e0d\u9069.<\/p><\/li>\r\n<\/ol>\r\n<p>\u4ee5\u4e0a\u3088\u308a\r\n\\[\r\n\\underline{( m, n ) = ( 12 , 9 )}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(2\\) \u4ee5\u4e0a\u306e\u6574\u6570 \\(m , n\\) \u306f \\(m^3+1^3 = n^3+10^3\\) \u3092\u307f\u305f\u3059. \\(m , n\\) \u3092\u6c42\u3081\u3088.","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":[45],"tags":[146,15],"class_list":["post-213","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2009","tag-hitotsubashi","tag-15"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/213","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=213"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/213\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=213"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=213"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=213"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}