{"id":1315,"date":"2015-10-19T00:53:24","date_gmt":"2015-10-18T15:53:24","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1315"},"modified":"2021-10-20T13:32:04","modified_gmt":"2021-10-20T04:32:04","slug":"ykr201504","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ykr201504\/","title":{"rendered":"\u6a2a\u56fd\u5927\u7406\u7cfb2015\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\u81ea\u7136\u6570\u3092 \\(2\\) \u500b\u4ee5\u4e0a\u306e\u9023\u7d9a\u3059\u308b\u81ea\u7136\u6570\u306e\u548c\u3067\u8868\u3059\u3053\u3068\u3092\u8003\u3048\u308b. \u305f\u3068\u3048\u3070, \\(42\\) \u306f \\(3 +4 + \\cdots +9\\) \u306e\u3088\u3046\u306b \\(2\\) \u500b\u4ee5\u4e0a\u306e\u9023\u7d9a\u3059\u308b\u81ea\u7136\u6570\u306e\u548c\u3067\u8868\u305b\u308b. \u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(2020\\) \u3092 \\(2\\) \u500b\u4ee5\u4e0a\u306e\u9023\u7d9a\u3059\u308b\u81ea\u7136\u6570\u306e\u548c\u3067\u8868\u3059\u8868\u3057\u65b9\u3092\u3059\u3079\u3066\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(a\\) \u3092 \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b\u3068\u304d, \\(2^a\\) \u306f \\(2\\) \u500b\u4ee5\u4e0a\u306e\u9023\u7d9a\u3059\u308b\u81ea\u7136\u6570\u306e\u548c\u3067\u8868\u305b\u306a\u3044\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(a , b\\) \u3092\u81ea\u7136\u6570\u3068\u3059\u308b\u3068\u304d, \\(2^a (2b+1)\\) \u306f \\(2\\) \u500b\u4ee5\u4e0a\u306e\u9023\u7d9a\u3059\u308b\u81ea\u7136\u6570\u306e\u548c\u3067\u8868\u305b\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

    \u81ea\u7136\u6570 \\(N\\) \u304c, \\(m \\ ( m \\geqq 1 )\\) \u3067\u59cb\u307e\u308b \\(k \\ (k \\geqq 2)\\) \u500b\u306e\u81ea\u7136\u6570\u306e\u548c\u3067\u8868\u305b\u308b\u6761\u4ef6\u3092\u8003\u3048\u308b.
    \r\n\\[\\begin{align}\r\nN & = m +(m+1) + \\cdots +(m+k-1) \\\\\r\n& = \\dfrac{k ( 2m+k-1 )}{2}\r\n\\end{align}\\]\r\n\u306a\u306e\u3067\r\n\\[\r\n2N = k ( 2m+k-1 ) \\quad ... [1]\r\n\\]\r\n\u3053\u3053\u3067, \u300c \\(k\\) \u3068 \\(2m+k-1\\) \u306f\u5947\u5076\u304c\u7570\u306a\u308b \u300d... [2] .
    \r\n\u307e\u305f, \\(m \\geqq 1\\) , \\(k \\geqq 2\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n2N & \\geqq k (k+1) \\gt k^2 \\\\\r\n\\text{\u2234} & \\quad 2 \\leqq k \\lt \\sqrt{2N} \\quad ... [3]\r\n\\end{align}\\]\r\n[2] [3] \u306b\u6ce8\u610f\u3057\u3066, [1] \u3092\u307f\u305f\u3059 \\(k , m\\) \u3092\u6c42\u3081\u308c\u3070\u3088\u3044.
    \r\n\\(N = 2020\\) \u306e\u3068\u304d\r\n\\[\r\n2N = 2^3 \\cdot 5 \\cdot 101 , \\ 31 \\lt \\sqrt{2N} = 2 \\sqrt{1010} \\lt 32\r\n\\]\r\n\u306a\u306e\u3067, \\(k\\) \u306e\u5019\u88dc\u306f\r\n\\[\r\nk = 5 , 8 , 40\r\n\\]\r\n- \\(k = 5\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\n2m +4 &= 808 \\\\\r\n\\text{\u2234} \\quad m & = 402\r\n\\end{align}\\]\r\n- \\(k = 8\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\n2m +7 &= 505 \\\\\r\n\\text{\u2234} \\quad m & = 299\r\n\\end{align}\\]\r\n- \\(k = 40\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\n2m +39 &= 101 \\\\\r\n\\text{\u2234} \\quad m & = 31\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u8868\u3057\u65b9\u306f, \u4ee5\u4e0b\u306e \\(3\\) \u901a\u308a.\r\n\\[\r\n2020 = \\underline{\\left\\{ \\begin{array}{l}402 +403 +\\cdots +406 \\\\ 299 +300 +\\cdots +306 \\\\ 31 +32 +\\cdots +70 \\end{array} \\right.}\r\n\\]\r\n

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

    \\(N = 2^a\\) \u306e\u3068\u304d, [1] \u3088\u308a\r\n\\[\r\n2^{a+1} = k ( 2m +k -1 )\r\n\\]\r\n[2] \u3088\u308a, \\(k = 1\\) \u3060\u3051\u304c\u5019\u88dc\u3067\u3042\u308b\u304c, [3] \u3092\u307f\u305f\u3055\u305a\u4e0d\u9069.
    \r\n\u3088\u3063\u3066, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n

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

    \\(N = 2^a (2b+1)\\) \u306e\u3068\u304d, [1] \u3088\u308a\r\n\\[\r\n2^{a+1} (2b+1) = k ( 2m +k -1 )\r\n\\]\r\n[2] [3] \u306b\u6ce8\u610f\u3059\u308c\u3070, \u3053\u308c\u3092\u307f\u305f\u3059 \\(k , m\\) \u306e\u7d44\u3068\u3057\u3066\r\n\\[\r\n( k , m ) = ( 2b+1 , 2^a -b )\r\n\\]\r\n\u304c\u5b58\u5728\u3059\u308b.
    \r\n\u3088\u3063\u3066, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\u81ea\u7136\u6570\u3092 \\(2\\) \u500b\u4ee5\u4e0a\u306e\u9023\u7d9a\u3059\u308b\u81ea\u7136\u6570\u306e\u548c\u3067\u8868\u3059\u3053\u3068\u3092\u8003\u3048\u308b. \u305f\u3068\u3048\u3070, \\(42\\) \u306f \\(3 +4 + \\cdots +9\\) \u306e\u3088\u3046\u306b \\(2\\) \u500b\u4ee5\u4e0a\u306e\u9023\u7d9a\u3059\u308b\u81ea\u7136\u6570\u306e\u548c\u3067\u8868\u305b\u308b. \u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\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":[133],"tags":[137,9],"class_list":["post-1315","post","type-post","status-publish","format-standard","hentry","category-yokokoku_r_2015","tag-137","tag-yokokoku_r"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1315","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=1315"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1315\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1315"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1315"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1315"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}