[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki3\/archives\/5582#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki3\/archives\/5582","headline":"\u81ea\u5df1\u540c\u5f62\u6570 &#8211; Wikipedia","name":"\u81ea\u5df1\u540c\u5f62\u6570 &#8211; Wikipedia","description":"\u81ea\u5df1\u540c\u5f62\u6570 (\u3058\u3053\u3069\u3046\u3051\u3044\u3059\u3046\u3001\u82f1: Automorphic number\uff09\u3068\u306f\u5e73\u65b9\u3057\u305f\u3068\u304d\u3001\u4e0b\u6841\u306e\u6570\u304c\u81ea\u5206\u81ea\u8eab\u3068\u540c\u3058\u306b\u306a\u308b\u6570\u306e\u4e8b\u3067\u3042\u308b\u3002 \u4f8b\u3048\u3070 52 = 25, 62 = 36, 762 = 5776, \u305d\u3057\u3066 8906252 = 793212890625, \u305d\u308c\u3086\u3048 5,","datePublished":"2021-07-31","dateModified":"2021-07-31","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki3\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki3\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f62bbd31e8191c1311531cf068dcea011f072561","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f62bbd31e8191c1311531cf068dcea011f072561","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki3\/archives\/5582","about":["Wiki"],"wordCount":939,"articleBody":"\u81ea\u5df1\u540c\u5f62\u6570 (\u3058\u3053\u3069\u3046\u3051\u3044\u3059\u3046\u3001\u82f1: Automorphic number\uff09\u3068\u306f\u5e73\u65b9\u3057\u305f\u3068\u304d\u3001\u4e0b\u6841\u306e\u6570\u304c\u81ea\u5206\u81ea\u8eab\u3068\u540c\u3058\u306b\u306a\u308b\u6570\u306e\u4e8b\u3067\u3042\u308b\u3002\u4f8b\u3048\u3070 52 = 25, 62 = 36, 762 = 5776, \u305d\u3057\u3066 8906252 = 793212890625, \u305d\u308c\u3086\u3048 5, 6, 76 , 890625\u306f\u3059\u3079\u3066\u81ea\u5df1\u540c\u5f62\u6570\u3067\u3042\u308b\u3002\u5177\u4f53\u7684\u306a\u81ea\u5df1\u540c\u5f62\u6570\u306f 1, 5, 6, 25, 76, 376, 625, 9376, &#8230; \uff08\u30aa\u30f3\u30e9\u30a4\u30f3\u6574\u6570\u5217\u5927\u8f9e\u5178\u306e\u6570\u5217 A003226\uff09 \u3067\u3042\u308a\u3001\u7121\u6570\u306b\u5b58\u5728\u3059\u308b\u3053\u3068\u304c\u5206\u304b\u3063\u3066\u3044\u308b\u3002n > 1 \u3092\u6e80\u305f\u3059 k \u6841\u306e\u81ea\u5df1\u540c\u5f62\u6570\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d, \u9ad8\u3005 2k \u6841\u306e\u81ea\u5df1\u540c\u5f62\u6570 n&#8217; \u3092\u767a\u898b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002n\u2032=(3\u22c5n2\u22122\u22c5n3)\u00a0mod102k.{displaystyle n&#8217;=(3cdot n^{2}-2cdot n^{3}) {bmod {10^{2k}}},.}1 \u3088\u308a\u5927\u304d\u306a k \u306b\u5bfe\u5fdc\u3059\u308b2\u3064\u306e\u81ea\u5df1\u540c\u5f62\u6570\u304c\u3042\u308b\u30021\u3064\u306f\u672b\u5c3e\u306e\u4f4d\u304c5\u3067\u3082\u30461\u3064\u306f6\u3067\u3042\u308b\u3002\u305d\u3057\u3066\u305d\u308c\u3089\u306e\u6570\u306e1\u3064\u306f\u4ee5\u4e0b\u306e\u5f62\u306b\u306a\u3063\u3066\u3044\u308b\u3002n\u22610(mod2k),n\u22611(mod5k),{displaystyle nequiv 0{pmod {2^{k}}},quad nequiv 1{pmod {5^{k}}},,}\u305d\u3057\u3066\u3082\u30461\u3064\u306e\u81ea\u5df1\u540c\u5f62\u6570\u306e\u5f62\u306fn\u22611(mod2k),n\u22610(mod5k).{displaystyle nequiv 1{pmod {2^{k}}},quad nequiv 0{pmod {5^{k}}},.}2\u3064\u306e\u6570\u306e\u5408\u8a08\u306f 10k + 1 \u3068\u306a\u308b\u3002\u3053\u306e2\u3064\u306e\u6570\u3067\u5c0f\u3055\u306a\u65b9\u306e\u6570\u304c 10k\u22121 \u3088\u308a\u5c0f\u3055\u3044\u5834\u5408\u3001\u4f8b\u3048\u3070 k = 4 \u3067\u3042\u308b2\u3064\u306e\u6570\u306f9376\u3068625\u3067\u3042\u308b\u3002\u3053\u306e\u5834\u5408 k \u6841\u306e\u81ea\u5df1\u540c\u5f62\u6570\u306b\u3059\u308b\u305f\u3081\u306b\u5c0f\u3055\u306a\u65b9 (k \u6841\u672a\u6e80) \u306e\u6570\u306b\u305f\u308a\u306a\u3044\u5206\u306e\u6841\u3060\u3051\u4e0a\u4f4d\u6841\u306b0\u3092\u4ed8\u3051\u52a0\u3048\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002(\u4f8b\uff0e9376 + 0625 = 10001)\u4ee5\u4e0b\u306e\u8868\u306f2\u3064\u306e k \u6841\u306e\u81ea\u5df1\u540c\u5f62\u6570\u3092\u767a\u898b\u3059\u308b\u305f\u3081\u306b\u4f7f\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u3002(k \u2266 1000)12781 25400 13369 00860 34889 08436 40238 75765 93682 19796 26181 91783 35204 92704 19932 48752 37825 86714 82789 05344 89744 01426 12317 03569 95484 19499 44461 06081 46207 25403 65599 98271 58835 60350 49327 79554 07419 61849 28095 20937 53026 85239 09375 62839 14857 16123 67351 97060 92242 42398 77700 75749 55787 27155 97674 13458 99753 76955 15862 71888 79415 16307 56966 88163 52155 04889 82717 04378 50802 84340 84412 64412 68218 48514 15772 99160 34497 01789 23357 96684 99144 73895 66001 93254 58276 78000 61832 98544 26232 82725 75561 10733 16069 70158 64984 22229 12554 85729 87933 71478 66323 17240 55157 56102 35254 39949 99345 60808 38011 90741 53006 00560 55744 81870 96927 85099 77591 80500 75416 42852 77081 62011 35024 68060 58163 27617 16767 65260 93752 80568 44214 48619 39604 99834 47280 67219 06670 41724 00942 34466 19781 24266 90787 53594 46166 98508 06463 61371 66384 04902 92193 41881 90958 16595 24477 86184 61409 12878 29843 84317 03248 17342 88865 72737 66314 65191 04988 02944 79608 14673 76050 39571 96893 71467 18013 75619 05546 29968 14764 26390 39530 07319 10816 98029 38509 89006 21665 09580 86381 10005 57423 42323 08961 09004 10661 99773 92256 25991 82128 90625 \u30aa\u30f3\u30e9\u30a4\u30f3\u6574\u6570\u5217\u5927\u8f9e\u5178\u306e\u6570\u5217 A0182471\u3064\u306e\u81ea\u5df1\u540c\u5f62\u6570\u306f\u6700\u5f8c\u304b\u3089 k \u6841\u306e\u5217\u3092\u3068\u308b\u3053\u3068\u3067\u307f\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3001\u305d\u3057\u30662\u756a\u76ee\u306f\u305d\u306e\u6570\u3092 10k + 1 \u304b\u3089\u5f15\u304f\u3053\u3068\u306b\u3088\u3063\u3066\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002(\u4f8b\uff0e8\u6841\u306e\u5834\u5408\u306f\u6700\u5f8c\u304b\u30898\u6841\u3092\u3068\u308b\u3068 12890625 \u3053\u308c\u304c1\u3064\u3081\u306e\u81ea\u5df1\u540c\u5f62\u6570\u3001\u305d\u3057\u30662\u3064\u3081\u306f 100000001 \u2212 12890625 = 87109376 \u3068\u306a\u308b\u3002)\u305d\u306e\u4ed6\u306e\u6027\u8cea[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u5916\u90e8\u30ea\u30f3\u30af[\u7de8\u96c6]http:\/\/planetmath.org\/examplesof1automorphicnumbers"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki3\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki3\/archives\/5582#breadcrumbitem","name":"\u81ea\u5df1\u540c\u5f62\u6570 &#8211; 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