{"id":1943,"date":"2021-10-26T23:17:34","date_gmt":"2021-10-26T14:17:34","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=1943"},"modified":"2021-10-26T23:17:34","modified_gmt":"2021-10-26T14:17:34","slug":"tkb201604","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkb201604\/","title":{"rendered":"\u6771\u5927\u6587\u7cfb2016\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. \r\n\u305f\u3060\u3057, (1)<\/strong> \u306b\u3064\u3044\u3066\u306f, \u7d50\u8ad6\u306e\u307f\u3092\u66f8\u3051\u3070\u3088\u3044.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(n\\) \u3092\u6b63\u306e\u6574\u6570\u3068\u3059\u308b. \\(3^n\\) \u3092 \\(10\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u3092 \\(a_n\\) \u3068\u3059\u308b. \\(a_n\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(n\\) \u3092\u6b63\u306e\u6574\u6570\u3068\u3057, \u3059\u308b. \\(3^n\\) \u3092 \\(4\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u3092 \\(b_n\\) \u3068\u3059\u308b. \\(b_n\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u6570\u5217 \\(\\{ x_n \\}\\) \u3092\u6b21\u306e\u3088\u3046\u306b\u5b9a\u3081\u308b. \r\n\\[\r\nx_1 = 1 , \\quad x _ {n+1} = 3^{ x_n } \\ ( n = 1, 2, 3, \\cdots )\r\n\\]\r\n\\(x_{10}\\) \u3092 \\(10\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \\(3^4 \\equiv 81 \\equiv 1 \\ ( \\text{mod} \\ 10 )\\) \u306a\u306e\u3067\r\n\\[\r\na _ {n+4} = a_n\r\n\\]\r\n\u3088\u3063\u3066, \\(a_1 = 3\\) , \\(a_2 = 9\\) , \\(a_3 = 7\\) , \\(a_4 = 1\\) \u3088\u308a\r\n\\[\r\na_n = \\underline{\\left\\{ \\begin{array}{ll} 3 & ( \\ n \\equiv 1 \\ ( \\text{mod} \\ 4 ) \\ \\text{\u306e\u3068\u304d} \\ ) \\\\ 9 & ( \\ n \\equiv 2 \\ ( \\text{mod} \\ 4 ) \\ \\text{\u306e\u3068\u304d} \\ ) \\\\ 7 & ( \\ n \\equiv 3 \\ ( \\text{mod} \\ 4 ) \\ \\text{\u306e\u3068\u304d} \\ ) \\\\ 1 & ( \\ n \\equiv 0 \\ ( \\text{mod} \\ 4 ) \\ \\text{\u306e\u3068\u304d} \\ ) \\end{array} \\right.}\r\n\\]\r\n

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

    \\(3^2 \\equiv 9 \\equiv 1 \\ ( \\text{mod} \\ 4 )\\) \u306a\u306e\u3067\r\n\\[\r\nb _ {n+2} = b_n\r\n\\]\r\n\u3088\u3063\u3066, \\(b_1 = 3\\) , \\(b_2 = 1\\) \u3088\u308a\r\n\\[\r\nb_n = \\underline{\\left\\{ \\begin{array}{ll} 3 & ( \\ n \\ \\text{\u304c\u5947\u6570\u306e\u3068\u304d} \\ ) \\\\ 1 & ( \\ n \\ \\text{\u304c\u5076\u6570\u306e\u3068\u304d} \\ ) \\end{array} \\right.}\r\n\\]\r\n

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

    \u6761\u4ef6\u3088\u308a, \\(n \\geqq 2\\) \u306e\u3068\u304d, \\(x_n\\) \u306f \\(3\\) \u306e\u7d2f\u4e57\u306a\u306e\u3067, \u5947\u6570\u3067\u3042\u308b.
    \r\n\u3086\u3048\u306b, (2)<\/strong> \u306e\u7d50\u679c\u304b\u3089, \\(3^{x _n}\\) \u306f \\(4\\) \u3067\u5272\u308b\u3068 \\(3\\) \u4f59\u308b.
    \r\n\u3055\u3089\u306b, (1)<\/strong> \u306e\u7d50\u679c\u304b\u3089, \\(n \\geqq 3\\) \u306e\u3068\u304d, \\(x_n\\) \u306f \\(10\\) \u3067\u5272\u308b\u3068 \\(7\\) \u4f59\u308b.
    \r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u4f59\u308a\u306f\r\n\\[\r\n\\underline{7}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. \u305f\u3060\u3057, (1) \u306b\u3064\u3044\u3066\u306f, \u7d50\u8ad6\u306e\u307f\u3092\u66f8\u3051\u3070\u3088\u3044. (1)\u3000\\(n\\) \u3092\u6b63\u306e\u6574\u6570\u3068\u3059\u308b. \\(3^n\\) \u3092 \\(10\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u3092 \\(a_n\\) \u3068\u3059\u308b. \\(a_n\\) \u3092\u6c42\u3081\u3088. … \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":[160],"tags":[149,162],"class_list":["post-1943","post","type-post","status-publish","format-standard","hentry","category-tokyo_b_2016","tag-tokyo_b","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1943","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=1943"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1943\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1943"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1943"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1943"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}