{"id":1883,"date":"2021-09-18T15:31:38","date_gmt":"2021-09-18T06:31:38","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=1883"},"modified":"2021-09-18T15:31:38","modified_gmt":"2021-09-18T06:31:38","slug":"thr201602","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr201602\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2016\uff1a\u7b2c2\u554f"},"content":{"rendered":"<hr \/>\n<p>\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(6\\) \u4ee5\u4e0a\u306e\u6574\u6570 \\(n\\) \u306b\u5bfe\u3057\u3066\u4e0d\u7b49\u5f0f\r\n\\[\r\n2^n \\gt n^2 +7\r\n\\]\r\n\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u6570\u5b66\u7684\u5e30\u7d0d\u6cd5\u306b\u3088\u308a\u793a\u305b.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\u7b49\u5f0f\r\n\\[\r\np^q = q^p +7\r\n\\]\r\n\u3092\u6e80\u305f\u3059\u7d20\u6570\u306e\u7d44 \\(( p , q )\\) \u3092\u3059\u3079\u3066\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\u793a\u3057\u305f\u3044\u4e0d\u7b49\u5f0f\u3092 [A] \u3068\u304a\u304f.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(n = 6\\) \u306e\u3068\u304d\r\n\\[\r\n2^6 = 64 \\gt 43 = 6^2 +7 \\ .\r\n\\]\r\n\u306a\u306e\u3067, [A] \u304c\u6210\u7acb\u3059\u308b.<\/p><\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(n = k \\ ( k \\geqq 6 )\\) \u306e\u3068\u304d<br \/>\r\n[A] \u304c\u6210\u7acb\u3059\u308b, \u3059\u306a\u308f\u3061\r\n\\[\r\n2^k \\gt k^2 +7 \\quad ... [1]\r\n\\]\r\n\u3068\u4eee\u5b9a\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n2^{k+1} -( k+1 )^2 -7 & \\gt 2 ( k^2 +7 ) -k^2 -2k -8 \\quad ( \\text{\u2235} \\ [1] \\ ) \\\\\r\n& = k^2 -2k +6 \\\\\r\n& = ( k-1 )^2 +5 \\gt 0 \\ .\r\n\\end{align}\\]\r\n\u3059\u306a\u308f\u3061\r\n\\[\r\n2^{k+1} \\gt ( k+1 )^2 +7\r\n\\]\r\n\u3067, \\(n = k+1\\) \u306e\u3068\u304d\u3082 [A] \u304c\u6210\u7acb\u3059\u308b.<\/p><\/li>\r\n<\/ol>\r\n<p><strong>1*<\/strong> <strong>2*<\/strong> \u304b\u3089, \u6570\u5b66\u7684\u5e30\u7d0d\u6cd5\u306b\u3088\u308a, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n<p><strong>(2)<\/strong><\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(p = 2\\) \u306e\u3068\u304d\r\n\\[\r\n2^q = q^2 +7\r\n\\]\r\n\u4e21\u8fba\u306e\u5947\u5076\u3092\u8003\u3048\u308b\u3068, \\(q\\) \u306f\u5947\u6570\u3067\u3042\u308a, <strong>(1)<\/strong> \u306e\u7d50\u679c\u3088\u308a, \\(q \\leqq 5\\) \u306a\u306e\u3067, \\(q\\) \u306e\u5019\u88dc\u306f \\(3 , 5\\) \u306e\u307f.\r\n<ul>\r\n<li><p>\\(q=3\\) \u306e\u3068\u304d\r\n\\[\r\n2^3 = 8 \\neq 16 = 3^2 +7\r\n\\]\r\n\u3067\u4e0d\u9069.<\/p><\/li>\r\n<li><p>\\(q=5\\) \u306e\u3068\u304d\r\n\\[\r\n2^5 = 32 = 5^2 +7\r\n\\]\r\n\u3067\u9069\u3059\u308b.<\/p><\/li>\r\n<\/ul><\/p><\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(p\\) \u304c \\(3\\) \u4ee5\u4e0a\u306e\u7d20\u6570\u306e\u3068\u304d<br \/>\r\n\u4e21\u8fba\u306e\u5947\u5076\u3092\u8003\u3048\u308b\u3068 \\(q=2\\) \u3067\u3042\u308a\r\n\\[\r\np^2 = 2^p +7 \\ .\r\n\\]\r\n<strong>(1)<\/strong> \u306e\u7d50\u679c\u3088\u308a, \\(p \\geqq 6\\) \u306e\u3068\u304d\r\n\\[\r\np^2 \\lt 2^p -7 \\lt 2^p +7 \\ .\r\n\\]\r\n\u306a\u306e\u3067, \\(p\\) \u306e\u5019\u88dc\u306f \\(3 , 5\\) \u306e\u307f.\r\n<ul>\r\n<li><p>\\(p=3\\) \u306e\u3068\u304d\r\n\\[\r\n3^2 = 9 \\neq 15 = 2^3 +7\r\n\\]\r\n\u3067\u4e0d\u9069.<\/p><\/li>\r\n<li><p>\\(p=5\\) \u306e\u3068\u304d\r\n\\[\r\n5^2 = 25 \\neq 39 = 2^5 +7\r\n\\]\r\n\u3067\u4e0d\u9069.<\/p><\/li>\r\n<\/ul><\/p><\/li>\r\n<\/ol>\r\n<p>\u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u7d44\u306f\r\n\\[\r\n( p , q ) = \\underline{( 2 , 5 )} \\ .\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. (1)\u3000\\(6\\) \u4ee5\u4e0a\u306e\u6574\u6570 \\(n\\) \u306b\u5bfe\u3057\u3066\u4e0d\u7b49\u5f0f \\[ 2^n \\gt n^2 +7 \\] \u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u6570\u5b66\u7684\u5e30\u7d0d\u6cd5\u306b\u3088\u308a\u793a\u305b. (2)\u3000\u7b49\u5f0f \\[ p^q = q^p +7 \\] \u3092 &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/thr201602\/\">\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":[155],"tags":[148,162],"class_list":["post-1883","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2016","tag-tohoku_r","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1883","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=1883"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1883\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1883"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1883"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1883"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}