{"id":319,"date":"2012-02-25T12:51:56","date_gmt":"2012-02-25T03:51:56","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=319"},"modified":"2021-11-04T14:46:21","modified_gmt":"2021-11-04T05:46:21","slug":"htb200801","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb200801\/","title":{"rendered":"\u4e00\u6a4b\u59272008\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\\(k\\) \u3092\u6b63\u306e\u6574\u6570\u3068\u3059\u308b.\r\n\\(5n^2-2kn+1 \\lt 0\\) \u3092\u307f\u305f\u3059\u6574\u6570 \\(n\\) \u304c, \u3061\u3087\u3046\u3069 \\(1\\) \u500b\u3067\u3042\u308b\u3088\u3046\u306a \\(k\\) \u3092\u3059\u3079\u3066\u6c42\u3081\u3088.<\/p>\r\n

\r\n\r\n

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

\\(5n^2-2kn+1 \\lt 0\\) ... [1] \u304c\u89e3\u3092\u3082\u3064\u306e\u306f, \u5224\u5225\u5f0f \\(D\\) \u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\n\\dfrac{D}{4} = k^2 -5 & \\geqq 0 \\\\\r\n\\text{\u2234} \\quad k & \\geqq \\sqrt{5} \\quad ... [2]\r\n\\end{align}\\]\r\n\u3053\u306e\u3068\u304d, [1] \u3092\u89e3\u304f\u3068\r\n\\[\r\n\\dfrac{k -\\sqrt{k^2 -5}}{5} \\lt n \\lt \\dfrac{k +\\sqrt{k^2 -5}}{5} \\quad ... [3]\r\n\\]\r\n\u3053\u306e\u7bc4\u56f2\u306b\u6574\u6570 \\(n\\) \u304c \\(1\\) \u3064\u3060\u3051\u542b\u307e\u308c\u308b\u305f\u3081\u306e\u6761\u4ef6\u306f, [3] \u306e\u5e45\u306b\u7740\u76ee\u3057\u3066\r\n\\[\\begin{align}\r\n0 & \\lt \\dfrac{k +\\sqrt{k^2 -5}}{5} -\\dfrac{k -\\sqrt{k^2 -5}}{5} \\leqq 2 \\\\\r\n0 & \\lt \\sqrt{k^2 -5} \\leqq 5 \\\\\r\n\\text{\u2234} \\quad k & \\leqq \\sqrt{30} \\quad ... [4]\r\n\\end{align}\\]\r\n[3] [4] \u3088\u308a, \u6761\u4ef6\u3092\u307f\u305f\u3059 \\(k\\) \u306e\u5019\u88dc\u306f\r\n\\[\r\nk = 3 , 4 , 5\r\n\\]\r\n

    \r\n

  1. 1*<\/strong>\u3000\\(k = 3\\) \u306e\u3068\u304d, [3] \u3088\u308a\r\n\\[\\begin{align}\r\n\\dfrac{3 -\\sqrt{4}}{5} & \\lt n \\lt \\dfrac{3 +\\sqrt{4}}{5} \\\\\r\n\\text{\u2234} \\quad \\dfrac{1}{5} & \\lt n \\lt 1\r\n\\end{align}\\]\r\n\u3053\u308c\u3092\u307f\u305f\u3059\u6574\u6570\u306f\u306a\u3044\u305f\u3081, \u4e0d\u9069.<\/p><\/li>\r\n

  2. 2*<\/strong>\u3000\\(k = 4\\) \u306e\u3068\u304d, [3] \u3088\u308a\r\n\\[\r\n\\dfrac{4 -\\sqrt{11}}{5} \\lt n \\lt \\dfrac{4 +\\sqrt{11}}{5}\r\n\\]\r\n\\(3 \\lt \\sqrt{11} \\lt 4\\) \u306a\u306e\u3067, \u3053\u308c\u3092\u307f\u305f\u3059\u6574\u6570\u306f \\(n = 1\\) \u306e\u307f.<\/p><\/li>\r\n

  3. 3*<\/strong>\u3000\\(k = 5\\) \u306e\u3068\u304d, [3] \u3088\u308a\r\n\\[\r\n\\dfrac{5 -\\sqrt{20}}{5} \\lt n \\lt \\dfrac{5 +\\sqrt{20}}{5}\r\n\\]\r\n\\(4 \\lt \\sqrt{20} \\lt 5\\) \u306a\u306e\u3067, \u3053\u308c\u3092\u307f\u305f\u3059\u6574\u6570\u306f \\(n = 1\\) \u306e\u307f.<\/p><\/li>\r\n<\/ol>\r\n

    \u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u6574\u6570\u306f\r\n\\[\r\nk = \\underline{4 , 5}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(k\\) \u3092\u6b63\u306e\u6574\u6570\u3068\u3059\u308b. \\(5n^2-2kn+1 \\lt 0\\) \u3092\u307f\u305f\u3059\u6574\u6570 \\(n\\) \u304c, \u3061\u3087\u3046\u3069 \\(1\\) \u500b\u3067\u3042\u308b\u3088\u3046\u306a \\(k\\) \u3092\u3059\u3079\u3066\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":[57],"tags":[146,16],"class_list":["post-319","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2008","tag-hitotsubashi","tag-16"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/319","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=319"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/319\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=319"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=319"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=319"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}