{"id":161,"date":"2011-12-01T18:18:32","date_gmt":"2011-12-01T09:18:32","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=161"},"modified":"2021-11-04T09:43:11","modified_gmt":"2021-11-04T00:43:11","slug":"htb201004","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb201004\/","title":{"rendered":"\u4e00\u6a4b\u59272010\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570 \\(a _ 1 , a _ 2\\) \u304c\u3042\u305f\u3048\u3089\u308c\u305f\u3068\u304d, \u6570\u5217 \\(\\left\\{ a _ n \\right\\}\\) \u3092\r\n\\[\r\na _ {n+2} = a _ {n+1} + 6a _ n\r\n\\]\r\n\u306b\u3088\u308a\u5b9a\u3081\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(a _ 1 = 1\\) , \\(a _ 2 = 2\\) \u306e\u3068\u304d, \\(a _ {2010}\\) \u3092 \\(10\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(a _ 2 = 3a _ 1\\) \u306e\u3068\u304d, \\(a _ {n+4} - a _ n\\) \u306f \\(10\\) \u306e\u500d\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

    (1)<\/strong><\/p>\r\n

    \\(r _ n \\equiv a _ n \\ ( \\text{mod} \\ 10 )\\) \u3068\u3059\u308c\u3070\r\n\\[\r\nr _ {n+2} \\equiv r _ {n+1} + r _ n \\quad ( \\text{mod} \\ 10 )\r\n\\]\r\n\u3053\u308c\u3092\u7528\u3044\u308b\u3068\r\n\\[\\begin{align}\r\n& \\begin{array}{c|cccccccc} n & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\\\ \\hline r _ n & 1 & 2 & 8 & 0 & 8 & 8 & 6 & 4 \\\\ \\end{array} \\\\\r\n& \\quad \\begin{array}{c|cccccccc} n & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 \\\\ \\hline r _ n & 0 & 4 & 4 & 8 & 2 & 0 & 2 & 2 \\\\ \\end{array} \\\\\r\n& \\qquad \\begin{array}{c|ccccccc} n & 17 & 18 & 19 & 20 & 21 & 22 & 23 \\\\ \\hline r _ n & 4 & 6 & 0 & 6 & 6 & 2 & 8 \\\\ \\end{array}\r\n\\end{align}\\]\r\n\u3053\u3053\u3067 \\(\\left( r _ 2 , r _ 3 \\right) = \\left( r _ {22} , r _ {23} \\right)\\) \u306a\u306e\u3067, \u4ee5\u5f8c \\(\\left\\{ r _ n \\right\\}\\) \u306f\u5468\u671f \\(20\\) \u3067\u7e70\u8fd4\u3059.
    \r\n\\(2010 = 1 +20 \\cdot 100 +9\\) \u306a\u306e\u3067\r\n\\[\r\nr _ {2010} = r _ {10} = 4\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6c42\u3081\u308b\u5024\u306f \\(\\underline{4}\\) .<\/p>\r\n

    (2)<\/strong><\/p>\r\n

    \u6761\u4ef6\u3088\u308a\r\n\\[\r\n\\begin{array}{c|cccccc} n & 1 & 2 & 3 & 4 & 5 & 6 \\\\ \\hline r _ n & r _ 1 & 3r _ 1 & 9r _ 1 & 7r _ 1 & r _ 1 & 3r _ 1 \\\\ \\end{array}\r\n\\]\r\n\u3053\u3053\u3067 \\(\\left( r _ 6 , r _ 5 \\right) = \\left( r _ 2 , r _ 1 \\right)\\) \u306a\u306e\u3067, \u4ee5\u5f8c \\(\\left\\{ r _ n \\right\\}\\) \u306f\u5468\u671f \\(4\\) \u3067\u7e70\u8fd4\u3059.
    \r\n\u3057\u305f\u304c\u3063\u3066, \u81ea\u7136\u6570 \\(k\\) \u306b\u5bfe\u3057\u3066\r\n\\[\r\nr _ {k+4} -r _ k = 0\r\n\\]\r\n\u3086\u3048\u306b, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570 \\(a _ 1 , a _ 2\\) \u304c\u3042\u305f\u3048\u3089\u308c\u305f\u3068\u304d, \u6570\u5217 \\(\\left\\{ a _ n \\right\\}\\) \u3092 \\[ a _ {n+2} = a _ {n+1} + 6a _ n \\] … \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":[46],"tags":[146,14],"class_list":["post-161","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2010","tag-hitotsubashi","tag-14"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/161","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=161"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/161\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=161"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=161"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=161"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}