{"id":1246,"date":"2015-08-22T20:19:03","date_gmt":"2015-08-22T11:19:03","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1246"},"modified":"2021-09-24T17:27:56","modified_gmt":"2021-09-24T08:27:56","slug":"tok201505","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tok201505\/","title":{"rendered":"\u6771\u5de5\u59272015\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\\(n\\) \u3092\u76f8\u7570\u306a\u308b\u7d20\u6570 \\(p _ 1 , p _ 2 , \\cdots , p _ k \\ ( k \\geqq 1 )\\) \u306e\u7a4d\u3068\u3059\u308b. \\(a , b\\) \u3092 \\(n\\) \u306e\u7d04\u6570\u3068\u3059\u308b\u3068\u304d, \\(a , b\\) \u306e\u6700\u5927\u516c\u7d04\u6570\u3092 \\(G\\) , \u6700\u5c0f\u516c\u500d\u6570\u3092 \\(L\\) \u3068\u3057,\r\n\\[\r\nf (a,b) = \\dfrac{L}{G}\r\n\\]\r\n\u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(f (a,b)\\) \u304c \\(n\\) \u306e\u7d04\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(f (a,b) = b\\) \u306a\u3089\u3070, \\(a = 1\\) \u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(m\\) \u3092\u81ea\u7136\u6570\u3068\u3059\u308b\u3068\u304d, \\(m\\) \u306e\u7d04\u6570\u3067\u3042\u308b\u3088\u3046\u306a\u7d20\u6570\u306e\u500b\u6570\u3092 \\(S(m)\\) \u3068\u3059\u308b. \\(S( f (a,b) ) +S(a) +S(b)\\) \u304c\u5076\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

    \\(a = G k\\) , \\(b = G \\ell\\) \uff08 \\(k , \\ell\\) \u306f \\(n\\) \u306e\u7d04\u6570\u3067, \u4e92\u3044\u306b\u7d20 ... [1] \uff09\u3068\u8868\u305b\u308b.
    \r\n\u3053\u306e\u3068\u304d \\(L = G k \\ell\\) \u306a\u306e\u3067\r\n\\[\r\nf(a,b) = \\dfrac{G k \\ell}{G} = k \\ell\r\n\\]\r\n[1] \u3088\u308a, \\(k \\ell \\leqq n\\) \u306a\u306e\u3067, \u3053\u308c\u306f \\(n\\) \u306e\u7d04\u6570\u3067\u3042\u308b.<\/p>\r\n

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

    \u6761\u4ef6\u3088\u308a\r\n\\[\\begin{align}\r\nf(a,b) = k \\ell & = b = G \\ell \\\\\r\n\\text{\u2234} \\quad k & = G\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\r\na = k^2\r\n\\]\r\n\\(k \\neq 1\\) \u3068\u4eee\u5b9a\u3059\u308b\u3068, \\(n\\) \u304c \\({p _ k}^2\\) \u3067\u5272\u308a\u5207\u308c\u308b\u3053\u3068\u306b\u306a\u308a, \u6761\u4ef6\u306b\u77db\u76fe\u3059\u308b.
    \r\n\u3088\u3063\u3066\r\n\\[\r\nk = 1\r\n\\]\r\n\u3059\u306a\u308f\u3061\r\n\\[\r\na = 1\r\n\\]\r\n

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

    (1)<\/strong> \u306e\u7d50\u679c\u3068 [1] \u304b\u3089\r\n\\[\r\nS( f(a,b) ) = S(k) +S( \\ell )\r\n\\]\r\n\u6761\u4ef6\u304b\u3089, \\(G\\) \u3068 \\(k\\) , \\(G\\) \u3068 \\(\\ell\\) \u3082\u3068\u3082\u306b\u4e92\u3044\u306b\u7d20\u306a\u306e\u3067\r\n\\[\r\nS(a) = S(G) +S(k) , \\ S(b) = S(G) +S( \\ell )\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\r\nS( f (a,b) ) +S(a) +S(b) = 2 ( S(G) +S(k) +S( \\ell ) )\r\n\\]\r\n\u3088\u3063\u3066, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\\(n\\) \u3092\u76f8\u7570\u306a\u308b\u7d20\u6570 \\(p _ 1 , p _ 2 , \\cdots , p _ k \\ ( k \\geqq 1 )\\) \u306e\u7a4d\u3068\u3059\u308b. \\(a , b\\) \u3092 \\(n\\) \u306e\u7d04\u6570\u3068\u3059\u308b\u3068\u304d, \\(a , b\\) … \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":[128],"tags":[141,137],"class_list":["post-1246","post","type-post","status-publish","format-standard","hentry","category-toko_2015","tag-toko","tag-137"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1246","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=1246"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1246\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1246"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1246"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1246"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}