{"id":1964,"date":"2021-11-14T09:49:43","date_gmt":"2021-11-14T00:49:43","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=1964"},"modified":"2021-11-14T13:40:06","modified_gmt":"2021-11-14T04:40:06","slug":"tkr202104","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkr202104\/","title":{"rendered":"\u6771\u5927\u7406\u7cfb2021\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\u4ee5\u4e0b\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u6b63\u306e\u5947\u6570 \\(K , L\\) \u3068\u6b63\u306e\u6574\u6570 \\(A , B\\) \u304c \\(KA = LB\\) \u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u3068\u3059\u308b.\r\n\\(K\\) \u3092 \\(4\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u304c \\(L\\) \u3092 \\(4\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u3068\u7b49\u3057\u3044\u306a\u3089\u3070,\r\n\\(A\\) \u3092 \\(4\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u306f \\(B\\) \u3092 \\(4\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u3068\u7b49\u3057\u3044\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u6b63\u306e\u6574\u6570 \\(a , b\\) \u304c \\(a \\gt b\\) \u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u3068\u3059\u308b.\r\n\u3053\u306e\u3068\u304d, \\(A = {} _ {4a+1} \\text{C} {} _ {4b+1}\\) , \\(B = {} _ {a} \\text{C} {} _ {b}\\) \u306b\u5bfe\u3057\u3066\r\n\\(KA =LB\\) \u3068\u306a\u308b\u3088\u3046\u306a\u6b63\u306e\u5947\u6570 \\(K , L\\) \u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(a , b\\) \u306f (2)<\/strong> \u306e\u901a\u308a\u3068\u3057, \u3055\u3089\u306b \\(a-b\\) \u304c \\(2\\) \u3067\u5272\u308a\u5207\u308c\u308b\u3068\u3059\u308b.\r\n\\({} _ {4a+1} \\text{C} {} _ {4b+1}\\) \u3092 \\(4\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u306f \\({} _ {a} \\text{C} {} _ {b}\\) \u3092 \\(4\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u3068\u7b49\u3057\u3044\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  4. (4)<\/strong>\u3000\\({} _ {2021} \\text{C} {} _ {37}\\) \u3092 \\(4\\) \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

    \\(K\\) \u3068 \\(L\\) \u306f\u5947\u6570\u3067, \\(4\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u304c\u7b49\u3057\u3044\u306e\u3067, \\(K = 4k \\pm 1\\) , \\(L = 4 \\ell \\pm 1\\) \uff08\u8907\u53f7\u540c\u9806, \\(k , \\ell\\) \u306f\u81ea\u7136\u6570\uff09\u3068\u304a\u3051\u308b.
    \r\n\\(A , B\\) \u3092 \\(4\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u3092\u305d\u308c\u305e\u308c \\(m , n\\) \u3068\u3059\u308c\u3070, \\(A = 4a' +m\\) , \\(B = 4b' +n\\) \uff08\\(a' , b'\\) \u306f\u81ea\u7136\u6570\uff09\u3068\u8868\u305b\u308b.\r\n\\[\\begin{align}\r\nKA & = 4 ( 4 k a' \\pm a' +km ) \\pm m \\ , \\\\\r\nLB & = 4 ( 4 \\ell b' \\pm b' +\\ell n ) \\pm n\r\n\\end{align}\\]\r\n\\(KA = LB\\) \u3067\u3042\u308c\u3070, \\(KA , LB\\) \u3092 \\(4\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u306f\u7b49\u3057\u3044\u306e\u3067\r\n\\[\\begin{align}\r\n\\pm m & = \\pm n \\\\\r\n\\text{\u2234} \\quad m & = n\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n

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

    \\(B = \\dfrac{a ( a-1 ) \\cdots ( a-b+1 )}{b ( 4b-1 ) \\cdots 1}\\) \u3067\u3042\u308b\u3053\u3068\u3092\u7528\u3044\u308c\u3070, \\(0 \\leqq k \\leqq b-1\\) \u3068\u3057\u3066\r\n\\[\\begin{align}\r\nA & = \\dfrac{4a+1}{4b+1} \\cdot \\dfrac{4a}{4b} \\cdot \\dfrac{4a-1}{4b-1} \\cdot \\dfrac{4a-2}{4b-2} \\cdot \\dfrac{4a-3}{4b-3} \\cdots \\\\\r\n& \\qquad \\cdots \\dfrac{4(a-k)}{4(b-k)} \\cdot \\dfrac{4(a-k)-1}{4(b-k)-1} \\cdot \\dfrac{4(a-k)-2}{4(b-k)-2} \\cdot \\dfrac{4(a-k)-3}{4(b-k)-3} \\cdots \\\\\r\n& \\qquad \\cdots \\dfrac{4(a-b)+4}{4} \\cdot \\dfrac{4(a-b)+3}{3} \\cdot \\dfrac{4(a-b)+2}{2} \\cdot \\dfrac{4(a-b)+1}{1} \\\\\r\n& = \\dfrac{4a+1}{4b+1} \\cdot \\dfrac{a}{b} \\cdot \\dfrac{4a-1}{4b-1} \\cdot \\dfrac{2a-1}{2b-1} \\cdot \\dfrac{4a-3}{4b-3} \\cdots \\\\\r\n& \\qquad \\cdots \\dfrac{a-k}{b-k} \\cdot \\dfrac{4(a-k)-1}{4(b-k)-1} \\cdot \\dfrac{2(a-k)-1}{2(b-k)-1} \\cdot \\dfrac{4(a-k)-3}{4(b-k)-3} \\cdots \\\\\r\n& \\qquad \\cdots \\dfrac{a-b+1}{1} \\cdot \\dfrac{4(a-b)+3}{3} \\cdot \\dfrac{2(a-b)+1}{1} \\cdot \\dfrac{4(a-b)+1}{1} \\\\\r\n& = B \\underline{\\left( \\dfrac{4a+1}{4b+1} \\cdot \\dfrac{4a-1}{4b-1} \\cdot \\dfrac{4a-3}{4b-3} \\cdots \\dfrac{4(a-k)-1}{4(b-k)-1} \\cdot \\dfrac{4(a-k)-3}{4(b-k)-3} \\cdots \\right.} \\\\\r\n& \\qquad \\underline{\\left.\\dfrac{4(a-b)+3}{3} \\cdot \\dfrac{4(a-b)+1}{1} \\right)} _ {[1]} \\\\\r\n& \\qquad \\underline{\\left( \\dfrac{2a-1}{2b-1} \\cdots \\dfrac{2(a-k)-1}{2(b-k)-1} \\cdots \\dfrac{2(a-b)+1}{1} \\right)} _ {[2]}\r\n\\end{align}\\]\r\n\u3053\u3053\u3067, [1] [2] \u306e\u5206\u5b50, \u5206\u6bcd\u306f\u3059\u3079\u3066\u5947\u6570\u306e\u7a4d\u3067, \u5947\u6570\u3067\u3042\u308b\u3053\u3068\u304b\u3089\r\n\\[\r\n\\left\\{ \\begin{array}{l} K = ( \\ [1] \\text{\u306e\u5206\u5b50} \\ ) \\times ( \\ [2] \\text{\u306e\u5206\u5b50} \\ ) \\\\ L = ( \\ [1] \\text{\u306e\u5206\u6bcd} \\ ) \\times ( \\ [2] \\text{\u306e\u5206\u6bcd} \\ ) \\end{array} \\right. \\quad ... [3]\r\n\\]\r\n\u3068\u304a\u3051\u3070, \\(K , L\\) \u306f\u5947\u6570\u3067 \\(KA = LB\\) \u3092\u307f\u305f\u3059.
    \r\n\u3088\u3063\u3066, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n

    (3)<\/strong><\/p>\r\n[1] \u306b\u542b\u307e\u308c\u308b\u5404\u5206\u6570\u306f, \u5206\u6bcd\u3068\u5206\u5b50\u3092 \\(4\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u304c\u7b49\u3057\u3044.
    \r\n\\(a-b\\) \u304c \\(2\\) \u3067\u5272\u308a\u5207\u308c\u308b\u306e\u3067, \\(a = b +2p \\ ( \\ p \\text{\u306f\u6574\u6570} \\ )\\) \u3068\u304a\u3051\u3066\r\n\\[\r\n[2] = \\dfrac{4p+2b-1}{2b-1} \\cdots \\dfrac{4p+2(b-k)-1}{2(b-k)-1} \\cdots \\dfrac{4p+1}{1}\r\n\\]\r\n\u3086\u3048\u306b, [2] \u306b\u542b\u307e\u308c\u308b\u5404\u5206\u6570\u3082, \u5206\u6bcd\u3068\u5206\u5b50\u3092 \\(4\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u304c\u7b49\u3057\u3044.
    \r\n\u3057\u305f\u304c\u3063\u3066, [3] \u3088\u308a\\(K\\) \u3068 \\(L\\) \u306f \\(4\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u304c\u7b49\u3057\u3044.
    \r\n\u3088\u3063\u3066, (1)<\/strong> \u306e\u7d50\u679c\u3082\u7528\u3044\u308c\u3070, \\(A\\) \u3068 \\(B\\) \u306f \\(4\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u304c\u7b49\u3057\u304f\u306a\u308a, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n

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

    (3)<\/strong> \u306e\u7d50\u679c\u3092\u7528\u3044\u308c\u3070, \u6cd5\u3092 \\(4\\) \u3068\u3057\u3066\r\n\\[\\begin{align}\r\n{} _ {2021} \\text{C} {} _ {37} & \\equiv {} _ {505} \\text{C} {} _ {9} \\quad ( \\ \\text{\u2235} \\ 2021 = 4 \\cdot 505 +1 , 37 = 4 \\cdot 9 +1 \\ ) \\\\\r\n& \\equiv {} _ {126} \\text{C} {} _ {2} \\quad ( \\ \\text{\u2235} \\ 505 = 4 \\cdot 126 +1 , 9 = 4 \\cdot 2 +1 \\ ) \\\\\r\n& \\equiv \\dfrac{126 \\cdot 125}{2} \\equiv 63 \\cdot 125 \\\\\r\n& \\equiv -1 \\cdot 1 \\equiv -1\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u4f59\u308a\u306f\r\n\\[\r\n\\underline{3}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u4ee5\u4e0b\u306e\u554f\u306b\u7b54\u3048\u3088. (1)\u3000\u6b63\u306e\u5947\u6570 \\(K , L\\) \u3068\u6b63\u306e\u6574\u6570 \\(A , B\\) \u304c \\(KA = LB\\) \u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u3068\u3059\u308b. \\(K\\) \u3092 \\(4\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u304c \\(L\\) \u3092 \\(4\\) \u3067\u5272\u3063 … \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":[164],"tags":[139,165],"class_list":["post-1964","post","type-post","status-publish","format-standard","hentry","category-tokyo_r_2021","tag-tokyo_r","tag-165"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1964","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=1964"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1964\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1964"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1964"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1964"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}