{"id":4621,"date":"2025-07-20T10:00:46","date_gmt":"2025-07-20T01:00:46","guid":{"rendered":"https:\/\/winroadrikeijyuku.com\/oita\/?p=4621"},"modified":"2025-07-17T16:47:59","modified_gmt":"2025-07-17T07:47:59","slug":"%e4%b8%8d%e7%ad%89%e5%bc%8f%e3%81%ae%e8%a8%bc%e6%98%8e-%e8%87%aa%e7%84%b6%e6%95%b0%e3%81%ae%e6%9d%a1%e4%bb%b6%e3%82%92%e3%81%97%e3%81%a3%e3%81%8b%e3%82%8a%e6%8a%8a%e6%8f%a1%e3%81%97%e3%82%88%e3%81%86","status":"publish","type":"post","link":"https:\/\/winroadrikeijyuku.com\/oita\/2025\/07\/20\/%e4%b8%8d%e7%ad%89%e5%bc%8f%e3%81%ae%e8%a8%bc%e6%98%8e-%e8%87%aa%e7%84%b6%e6%95%b0%e3%81%ae%e6%9d%a1%e4%bb%b6%e3%82%92%e3%81%97%e3%81%a3%e3%81%8b%e3%82%8a%e6%8a%8a%e6%8f%a1%e3%81%97%e3%82%88%e3%81%86\/","title":{"rendered":"\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e (\u81ea\u7136\u6570\u306e\u6761\u4ef6\u3092\u3057\u3063\u304b\u308a\u628a\u63e1\u3057\u3088\u3046!) 2024\u4e5d\u5dde\u5927\u5165\u8a66\u3000| \u5927\u5206\u5e02 \u5927\u5b66\u53d7\u9a13 \u6570\u5b66 \u587e | \u5927\u5206\u7406\u7cfb\u5c02\u9580\u587eWINROAD"},"content":{"rendered":"

\u554f\u984c\u3000\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088\u3002<\/p>\n

(1) \u81ea\u7136\u6570a\u3001b\u304c a<b \u3092\u307f\u305f\u3059\u3068\u304d\u3001\u200b\\( \\dfrac{b!}{a!}\\geqq b \\)<\/span>\u200b\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u793a\u305b\u3002<\/p>\n

(2) \u200b\\( 2\\cdot a!=b! \\)<\/span>\u200b\u3092\u307f\u305f\u3059\u81ea\u7136\u6570\u306e\u7d44( a , b )\u3092\u3059\u3079\u3066\u6c42\u3081\u3088\u3002<\/p>\n

(3) \u200b\\( a!+b!=2\\cdot c! \\)<\/span>\u200b\u3092\u307f\u305f\u3059\u81ea\u7136\u6570\u306e\u7d44( a , b , c )\u3092\u3059\u3079\u3066\u6c42\u3081\u3088\u3002<\/p>\n

\n

(1) a,b\u304c\u81ea\u7136\u6570\u3067\u3042\u308aa<b\u306a\u306e\u3067\u200b\\( b\\geqq a+1 \\)<\/span>\u200b\u306a\u306e\u3067\u200b\\( b-1\\geqq a \\)<\/span><\/p>\n

\u3057\u305f\u304c\u3063\u3066\u200b\\( (b-1)!\\geqq a! \\)<\/span>\u200b<\/p>\n

\u200b\\( \u5de6\u8fba=\\dfrac{b!}{a!}\\geqq\\dfrac{b!}{(b-1)!}=b \\)<\/span>\u200b\u3088\u3063\u3066\u200b\\( \\dfrac{b!}{a!}\\geqq b \\)<\/span>\u8a3c\u660e\u7d42\u308f\u308a<\/p>\n

 <\/p>\n

(2) (1)\u306e\u7d50\u679c\u304b\u3089<\/p>\n

\u2460a<b\u306e\u3068\u304d\\( 2\\cdot a!=b! \\)<\/span>\u200b\u306e\u4e21\u8fba\u3092a!\u3067\u5272\u308b\u3068\u200b\\( 2=\\dfrac{b!}{a!} \\)<\/span>\u200b\u3064\u307e\u308a\u200b\\( 2\\geqq b \\)<\/span>\u200b\u3068\u306a\u308a<\/p>\n

b=1\u307e\u305f\u306fb=2\u3068\u306a\u308a\u307e\u3059\u3002a , b \u306f\u81ea\u7136\u6570\u3067 a<b \u306a\u306e\u3067b=2 \u3088\u3063\u3066( a , b )=(1 , 2)<\/p>\n

\u2461a=b\u306e\u3068\u304d\u200b\\( 2\\cdot a!=b! \\)<\/span>\u200b\u304c\u6210\u308a\u7acb\u305f\u306a\u3044\u306e\u3067a , b \u306f\u5b58\u5728\u3057\u306a\u3044\u3002<\/p>\n

\u2462a>b\u306e\u3068\u304d(1)\u3067a,b\u3092\u5165\u308c\u66ff\u3048\u3066\u200b\\( \\dfrac{a!}{b!}\\geqq a \\)<\/span>\u200b<\/p>\n

\\( 2\\cdot a!=b! \\)<\/span>\u200b\u306e\u4e21\u8fba\u3092\u200b\\( 2\\cdot b! \\)<\/span>\u200b\u3067\u5272\u308b\u3068\u200b\\( \\dfrac{a!}{b!}=\\dfrac{1}{2} \\)<\/span>\u200b<\/p>\n

\u200b\\( \\dfrac{1}{2}\\geqq a \\)<\/span>\u200b\u3068\u306a\u308a\u3053\u308c\u3092\u307f\u305f\u3059\u81ea\u7136\u6570a\u306f\u5b58\u5728\u3057\u306a\u3044\u3002<\/p>\n

\u2460\u3001\u2461\u3001\u2462\u3088\u308a( a , b )=(1 , 2)<\/p>\n

 <\/p>\n

(3) \u2460a<b \u306e\u3068\u304d\u200b\\( 2a!\\leqq a!+b!\\leqq 2b!\\\\2a!\\leqq 2c!\\leqq 2b! \\)<\/span>\u200b<\/p>\n

\u3068\u306a\u308b\u306e\u3067\u200b \u200b\\( a<c<b\\)<\/span>\u3001a , b , c\u306f\u81ea\u7136\u6570\u306a\u306e\u3067\u200b\\( c\\leqq b-1 \\)<\/span>\u200b<\/p>\n

\u200b\\( 2c!=a!+b!\u3000\u3088\u308a\u30002=\\dfrac{a!}{c!}+\\dfrac{b!}{c!}>\\dfrac{a!}{c!}+\\dfrac{b!}{(b-1)!}=\\dfrac{a!}{c!}+b \\)<\/span>\u200b<\/p>\n

\u200b\\( b<2 \\)<\/span>\u200b\u3068\u306a\u308a\u200b\\( b=1 \\)<\/span>\u200b\u3053\u306e\u3068\u304da<b\u3092\u6e80\u305f\u3059\u81ea\u7136\u6570a\u306f\u5b58\u5728\u3057\u306a\u3044\u3002<\/p>\n

\u2461 a>b\u306e\u3068\u304d\u2460\u3068\u540c\u69d8\u306b\\( a=1 \\)<\/span>\u200b\u3053\u306e\u3068\u304db<a\u3092\u6e80\u305f\u3059\u81ea\u7136\u6570b\u306f\u5b58\u5728\u3057\u306a\u3044\u3002<\/p>\n

\u2462a=b\u306e\u3068\u304d\\( a!+b!=2\\cdot c! \\\\2a!=2c!\\\\a=b=c\\)<\/span>\u200b<\/p>\n

\u3088\u3063\u3066(a , b , c )=( m , m , m )\u305f\u3060\u3057m\u306f\u81ea\u7136\u6570<\/p>\n

 <\/p>\n

\u81ea\u7136\u6570\u3067\u3042\u308b\u3053\u3068\u3068\u4e0d\u7b49\u5f0f\u6761\u4ef6\u3092\u3057\u3063\u304b\u308a\u628a\u63e1\u3057\u3066\u304a\u304b\u306a\u3044\u3068\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n

 <\/p>\n

 <\/p>\n

\uff08\u5927\u5206\u7406\u7cfb\u5c02\u9580\u587eWINROAD \u9996\u85e4\uff09<\/p>\n","protected":false},"excerpt":{"rendered":"

\u554f\u984c\u3000\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088\u3002 (1) \u81ea\u7136\u6570a\u3001b\u304c a<b \u3092\u307f\u305f\u3059\u3068\u304d\u3001\u200b\\( \\dfrac{b!}{a!}\\geqq b \\)\u200b\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u793a\u305b\u3002 (2) \u200b\\( 2\\cdot a!=b! \\)\u200b\u3092\u307f\u305f\u3059\u81ea<\/p>\n

\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"vkexunit_cta_each_option":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-4621","post","type-post","status-publish","format-standard","hentry","category-1"],"_links":{"self":[{"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/posts\/4621","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/comments?post=4621"}],"version-history":[{"count":26,"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/posts\/4621\/revisions"}],"predecessor-version":[{"id":4734,"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/posts\/4621\/revisions\/4734"}],"wp:attachment":[{"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/media?parent=4621"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/categories?post=4621"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/tags?post=4621"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}