{"id":1340,"date":"2015-12-29T00:43:11","date_gmt":"2015-12-28T15:43:11","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1340"},"modified":"2021-10-30T20:01:13","modified_gmt":"2021-10-30T11:01:13","slug":"tkb201501","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkb201501\/","title":{"rendered":"\u6771\u5927\u6587\u7cfb2015\uff1a\u7b2c1\u554f"},"content":{"rendered":"<hr \/>\n<p>\u4ee5\u4e0b\u306e\u547d\u984c <strong>A<\/strong> , <strong>B<\/strong> \u305d\u308c\u305e\u308c\u306b\u5bfe\u3057, \u305d\u306e\u771f\u507d\u3092\u8ff0\u3079\u3088.\r\n\u307e\u305f, \u771f\u306a\u3089\u3070\u8a3c\u660e\u3092\u4e0e\u3048, \u507d\u306a\u3089\u3070\u53cd\u4f8b\u3092\u4e0e\u3048\u3088.<\/p>\r\n<ol>\r\n<li><p>\u547d\u984c <strong>A<\/strong>\u3000\\(n\\) \u304c\u6b63\u306e\u6574\u6570\u306a\u3089\u3070, \\(\\dfrac{n^3}{26} +100 \\geqq n^2\\) \u304c\u6210\u308a\u7acb\u3064.<\/p><\/li>\r\n<li><p>\u547d\u984c <strong>B<\/strong>\u3000\u6574\u6570 \\(n , m , \\ell\\) \u304c \\(5n +5m +3 \\ell = 1\\) \u3092\u307f\u305f\u3059\u306a\u3089\u3070, \\(10nm +3m \\ell +3n \\ell \\lt 0\\) \u304c\u6210\u308a\u7acb\u3064.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p><strong>A<\/strong><\/p>\r\n<p>\u4e0e\u5f0f\u3092\u5909\u5f62\u3057\u3066\r\n\\[\r\nn^3 -26n^2 +2600 \\geqq 0\r\n\\]\r\n\u304c\u6210\u7acb\u3059\u308b\u304b, \u306b\u3064\u3044\u3066\u8003\u3048\u308c\u3070\u3088\u3044.<br \/>\r\n\\(f(x) = x^3 -26x^2 +2600\\) \u3068\u304a\u304f\u3068\r\n\\[\r\nf'(x) = 3x^2 -52x = 3x \\left( x -\\dfrac{52}{3} \\right)\r\n\\]\r\n\u306a\u306e\u3067, \\(x \\gt 0\\) \u306b\u304a\u3051\u308b \\(f(x)\\) \u306e\u5897\u6e1b\u306f\u4e0b\u8868\u306e\u3068\u304a\u308a.\r\n\\[\r\n\\begin{array}{c|cccc} x & (0) & \\cdots & \\dfrac{52}{3} & \\cdots \\\\ \\hline f'(x) & (0) & - & 0 & + \\\\ \\hline f(x) & & \\searrow & \\text{\u6700\u5c0f} & \\nearrow \\end{array}\r\n\\]\r\n\\(n\\) \u306f\u6574\u6570\u3067\u3042\u308a, \\(\\dfrac{52}{3} = 17 +\\dfrac{1}{3}\\) \u306a\u306e\u3067, \u6700\u5c0f\u5024\u306e\u5019\u88dc\u306f \\(f(17) , f(18)\\) .<br \/>\r\n\u3053\u3053\u3067\r\n\\[\\begin{align}\r\nf(17) & = 17^2 ( 17 -26 ) +2600 \\\\\r\n& = -9 \\cdot 289 +2600 = -1 \\lt 0\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u547d\u984c\u306f \\(\\underline{\\text{\u507d}}\\) \u3067\u3042\u308a, \u53cd\u4f8b\u306f \\(n = \\underline{17}\\) \u306e\u3068\u304d.<\/p>\r\n<p><strong>B<\/strong><\/p>\r\n<p>\\(K = 10nm +3m \\ell +3n\\) \u3068\u304a\u304f.<br \/>\r\n\u6761\u4ef6\u3088\u308a \\(3 \\ell = 1 -5(m+n)\\) ... [1] \u306a\u306e\u3067\r\n\\[\\begin{align}\r\nK & = 10nm +(m+n) \\{ 1 -5(m+n) \\} \\\\\r\n& = ( m -5m^2 ) +( n -5n^2 ) \\quad ... [2]\r\n\\end{align}\\]\r\n\u3053\u3053\u3067, \u6574\u6570 \\(k\\) \u306b\u3064\u3044\u3066<\/p>\r\n<ul>\r\n<li><p>\\(k \\neq 0\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\nk & \\leqq k^2 \\lt 5k^2 \\\\\r\n\\text{\u2234} \\quad & k -5k^2 \\lt 0\r\n\\end{align}\\]<\/li>\r\n<li><p>\\(k = 0\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\nk & = 5k^2 = 0 \\\\\r\n\\text{\u2234} \\quad & k -5k^2 = 0\r\n\\end{align}\\]<\/li>\r\n<\/ul>\r\n<p>\\(m = n = 0\\) \u306e\u3068\u304d, [1] \u3088\u308a \\(\\ell = \\dfrac{1}{3}\\) \u3067\u6574\u6570\u3067\u306a\u3044\u304b\u3089, \\(n , m\\) \u306e\u3044\u305a\u308c\u304b\u306f \\(0\\) \u3067\u306f\u306a\u3044.<br \/>\r\n\u3088\u3063\u3066, [2] \u3088\u308a\r\n\\[\r\nK \\lt 0\r\n\\]\r\n\u3059\u306a\u308f\u3061, \u547d\u984c\u306f \\(\\underline{\\text{\u771f}}\\) \u3067\u3042\u308b.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\u4ee5\u4e0b\u306e\u547d\u984c A , B \u305d\u308c\u305e\u308c\u306b\u5bfe\u3057, \u305d\u306e\u771f\u507d\u3092\u8ff0\u3079\u3088. \u307e\u305f, \u771f\u306a\u3089\u3070\u8a3c\u660e\u3092\u4e0e\u3048, \u507d\u306a\u3089\u3070\u53cd\u4f8b\u3092\u4e0e\u3048\u3088. \u547d\u984c A\u3000\\(n\\) \u304c\u6b63\u306e\u6574\u6570\u306a\u3089\u3070, \\(\\dfrac{n^3}{26} +100 \\geqq n^ &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/tkb201501\/\">\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":[135],"tags":[149,137],"class_list":["post-1340","post","type-post","status-publish","format-standard","hentry","category-tokyo_b_2015","tag-tokyo_b","tag-137"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1340","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=1340"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1340\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1340"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1340"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1340"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}