{"id":6846,"date":"2022-06-02T17:50:36","date_gmt":"2022-06-02T08:50:36","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=6846"},"modified":"2022-06-06T23:42:40","modified_gmt":"2022-06-06T14:42:40","slug":"mod","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/mod.html","title":{"rendered":"\u5408\u540c\u5f0f\uff08mod\uff09\uff1a\u8a08\u7b97\u65b9\u6cd5\u3068\u8a3c\u660e\u554f\u984c\u306e\u89e3\u304d\u65b9"},"content":{"rendered":"\n<p>\u6570\u5b66\u3067\u5b66\u3076\u5185\u5bb9\u306b\u5408\u540c\u5f0f\uff08mod\uff09\u304c\u3042\u308a\u307e\u3059\u3002\u9ad8\u6821\u6570\u5b66\u306e\u4e2d\u3067\u3082\u5fdc\u7528\u7de8\u3067\u3042\u308a\u3001\u6574\u6570\u306e\u5272\u308a\u7b97\u3067\u91cd\u8981\u3068\u306a\u308b\u5185\u5bb9\u304c\u5408\u540c\u5f0f\u3067\u3059\u3002\u6574\u6570\u306e\u5272\u308a\u7b97\u306b\u3064\u3044\u3066\u5546\u3068\u4f59\u308a\u3092\u6570\u5f0f\u3067\u8868\u3059\u3068\u304d\u3001\u5408\u540c\u5f0f\u3092\u5229\u7528\u3059\u308c\u3070\u4fbf\u5229\u3067\u3059\u3002<\/p>\n<p>\u7279\u306b\u8a3c\u660e\u554f\u984c\u3067\u5408\u540c\u5f0f\u306f\u975e\u5e38\u306b\u512a\u308c\u3066\u3044\u307e\u3059\u3002\u5408\u540c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u3001\u7c21\u5358\u306b\u8a3c\u660e\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u304b\u3089\u3067\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u5408\u540c\u5f0f\u3092\u5229\u7528\u3057\u3066\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u307e\u305f\u3001\u5408\u540c\u5f0f\u306e\u7279\u5fb4\u306b\u306f\u4f55\u304c\u3042\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<p>\u6574\u6570\u306e\u8a08\u7b97\u306f\u6570\u5b66\u3067\u91cd\u8981\u306a\u5185\u5bb9\u306e\u4e00\u3064\u3067\u3059\u3002\u305d\u3053\u3067\u5408\u540c\u5f0f\u3092\u5229\u7528\u3057\u3001\u8a08\u7b97\u3084\u8a3c\u660e\u3092\u884c\u3048\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<h2>\u5408\u540c\u5f0f\uff08mod\uff09\u3068\u306f\u3001\u5272\u308a\u7b97\u306e\u4f59\u308a\u3067\u5229\u7528\u3055\u308c\u308b\u7b49\u5f0f<\/h2>\n<p>\u307e\u305a\u3001\u5408\u540c\u5f0f\uff08mod\uff09\u3068\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002\u6574\u6570\u306e\u5272\u308a\u7b97\u306b\u3064\u3044\u3066\u3001\u5546\u3068\u4f59\u308a\u3092\u5229\u7528\u3057\u3066\u6570\u5f0f\u3067\u8868\u3059\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u8a18\u3057\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/06\/jfhw3.jpg\" alt=\"\" width=\"329\" height=\"168\" class=\"aligncenter size-full wp-image-6838\" \/><\/p>\n<p>\u305f\u3060\u3001\\(a=bq+r\\)\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3059\u308b\u3068\u3001\u8a08\u7b97\u904e\u7a0b\u304c\u7169\u96d1\u306b\u306a\u308a\u3084\u3059\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u4f59\u308a\u3060\u3051\u306b\u7740\u76ee\u3057\u305f\u5f0f\u304c\u958b\u767a\u3055\u308c\u307e\u3057\u305f\u3002\u305d\u308c\u304c\u5408\u540c\u5f0f\u3067\u3042\u308a\u3001<span style=\"color: #ff0000;\">\u5408\u540c\u5f0f\u3068\u306f\u300c\u5272\u308a\u7b97\u306e\u4f59\u308a\u306b\u7126\u70b9\u3092\u5f53\u3066\u305f\u5f0f\u300d\u3068\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n<p>\u4f8b\u3048\u3070\\(9=4\u00d72+1\\)\u3067\u3042\u308a\u3001\\(13=4\u00d73+1\\)\u3067\u3059\u3002\u3064\u307e\u308a9\u306813\u3092\u6bd4\u8f03\u3059\u308b\u3068\u304d\u30014\u3067\u5272\u308b\u3068\u4e21\u65b9\u3068\u3082\u4f59\u308a\u306f1\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u5408\u540c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/06\/jfhw8.jpg\" alt=\"\" width=\"363\" height=\"168\" class=\"aligncenter size-full wp-image-6848\" \/><\/p>\n<p>\u5408\u540c\u5f0f\u3067\u306f2\u3064\u306e\u8a18\u53f7\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u305d\u308c\u304c\u5408\u540c\uff08\u2261\uff09\u3068mod\uff08\u4f59\u308a\uff1amodulo\uff09\u3067\u3059\u3002\u4ee5\u4e0b\u304c\u5408\u540c\u5f0f\u306e\u4f8b\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\(5\u226115\\) \\((mod\\) \\(5)\\)<\/li>\n<li>\\(13\u22611\\) \\((mod\\) \\(3)\\)<\/li>\n<li>\\(15\u2261-1\\) \\((mod\\) \\(4)\\)<\/li>\n<li>\\(-3\u2261-11\\) \\((mod\\) \\(4)\\)<\/li>\n<\/ul>\n<p>\u306a\u304a\\(a\\)\u3068\\(b\\)\u306b\u3064\u3044\u3066\u3001\\(n\\)\u3067\u5272\u308b\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u73fe\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a\u2261b\\) \\((mod\\)\u00a0\\(n)\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u3068\u304d\u3001\u5272\u308b\u6570\\(n\\)\u3092\u300c\u6cd5\u300d\u3068\u3044\u3044\u307e\u3059\u3002\u307e\u305f\u4f59\u308a\u304c\u7b49\u3057\u3044\u5834\u5408\u3001\u8907\u6570\u306e\u5408\u540c\u5f0f\u3092\u3064\u306a\u3052\u3066\u3082\u554f\u984c\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>\\(4\u22617\u226110\\) \\((mod\\) \\(3)\\)<\/p>\n<p>\u5408\u540c\u5f0f\u3092\u5b66\u3076\u3068\u304d\u3001\u307e\u305a\u306f\u5408\u540c\u5f0f\u306e\u7279\u6709\u306e\u6570\u5f0f\u306e\u610f\u5473\u3092\u899a\u3048\u308b\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u5408\u540c\u5f0f\u306e\u4f5c\u308a\u65b9\uff1a\u30de\u30a4\u30ca\u30b9\u3092\u542b\u3080\u5408\u540c\u5f0f<\/h3>\n<p>\u305f\u3060\u3001\u5408\u540c\u5f0f\u3092\u4f5c\u308b\u306e\u306f\u8907\u96d1\u3067\u3059\u3002\u7279\u306b\u30de\u30a4\u30ca\u30b9\u3092\u542b\u3080\u5408\u540c\u5f0f\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u304b\u308f\u304b\u308a\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001\\(a-b\\)\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><span style=\"color: #0000ff;\">\\(a\\)\u3068\\(b\\)\u3092\\(n\\)\u3067\u5272\u308b\u3068\u304d\u3001\u4f59\u308a\u304c\u7b49\u3057\u3044\u3068\u3044\u3046\u306e\u306f\u3001\\(a-b\\)\u304c\\(n\\)\u306e\u500d\u6570\u306b\u306a\u308b\u306e\u3068\u610f\u5473\u304c\u540c\u3058\u3067\u3059\u3002<\/span>\u5408\u540c\u5f0f\u3092\u4f5c\u308b\u3068\u304d\u3001\\(a-b\\)\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\\(n\\)\u306e\u500d\u6570\u306b\u306a\u3063\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3059\u308b\u3068\u52b9\u7387\u7684\u3067\u3059\u3002<\/p>\n<p>\u3053\u306e\u8003\u3048\u65b9\u3092\u5229\u7528\u3059\u308c\u3070\u3001\u30de\u30a4\u30ca\u30b9\u3092\u542b\u3080\u5834\u5408\u3067\u3042\u3063\u3066\u3082\u5408\u540c\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002\u4f8b\u3048\u3070\\(-3\u2261-11\\) \\((mod\\) \\(4)\\)\u306e\u5834\u5408\u3001\\(-3-(-11)=8\\)\u3068\u306a\u308a\u30014\u306e\u500d\u6570\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u30d2\u30f3\u30c8\u306a\u3057\u306b\u30de\u30a4\u30ca\u30b9\u3092\u542b\u3080\u5408\u540c\u5f0f\u3092\u4f5c\u308b\u306e\u306f\u96e3\u3057\u3044\u305f\u3081\u3001\\(a-b\\)\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\\(n\\)\u500d\u306b\u306a\u3063\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><span style=\"color: #0000ff;\">\u306a\u305c\\(a-b\\)\u304c\u6709\u52b9\u304b\u3068\u3044\u3046\u3068\u3001\u4f59\u308a\u304c\u540c\u3058\u3060\u304b\u3089\u3067\u3059\u3002<\/span>\u4f59\u308a\u304c\u540c\u3058\u5834\u5408\u3001\\(a-b\\)\u306b\u3088\u3063\u3066\u4f59\u308a\u304c\u6d88\u3048\u307e\u3059\u3002\u3053\u308c\u306f\u3064\u307e\u308a\u3001\\(n\\)\u306e\u500d\u6570\u306b\u306a\u308b\u3053\u3068\u3068\u610f\u5473\u304c\u540c\u3058\u3067\u3059\u3002\u5408\u540c\u5f0f\u306b\u30de\u30a4\u30ca\u30b9\u304c\u542b\u307e\u308c\u308b\u30b1\u30fc\u30b9\u306b\u9650\u3089\u305a\u3001\u5408\u540c\u5f0f\u3067\\(a-b\\)\u3092\u5229\u7528\u3059\u308b\u306e\u306f\u5f79\u306b\u7acb\u3064\u306e\u3067\u3059\u3002<\/p>\n<h2>\u5408\u540c\u5f0f\u3067\u5229\u7528\u3055\u308c\u308b\u6027\u8cea<\/h2>\n<p>\u306a\u304a\u3001\u5408\u540c\u5f0f\u3067\u5229\u7528\u3055\u308c\u308b\u4e3b\u306a\u6027\u8cea\u304c\u3042\u308a\u3001\u3053\u308c\u3092\u899a\u3048\u308b\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002\u5408\u540c\u5f0f\u306b\u306f\u4ee5\u4e0b\u306e\u6027\u8cea\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u5408\u540c\u5f0f\u3092\u5229\u7528\u3057\u3066\u8db3\u3057\u7b97\u3001\u5f15\u304d\u7b97\u3001\u304b\u3051\u7b97\u3092\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b<\/li>\n<li>\u4e92\u3044\u306b\u7d20\u306e\u5834\u5408\u3001\u5408\u540c\u5f0f\u3092\u5229\u7528\u3057\u3066\u5272\u308a\u7b97\u304c\u3067\u304d\u308b<\/li>\n<li>\u3079\u304d\u4e57\u6570\u3067\u306f\u3001\u5408\u540c\u5f0f\u306b\u6307\u6570\u3092\u52a0\u3048\u3066\u3082\u4f59\u308a\u306f\u540c\u3058<\/li>\n<\/ul>\n<p>\u305d\u308c\u305e\u308c\u306e\u5185\u5bb9\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u5408\u540c\u5f0f\u3067\u306e\u8db3\u3057\u7b97\u3001\u5f15\u304d\u7b97\u3001\u304b\u3051\u7b97<\/h3>\n<p>2\u3064\u306e\u5408\u540c\u5f0f\u306b\u3064\u3044\u3066\u3001\u8db3\u3057\u7b97\u3084\u5f15\u304d\u7b97\u3001\u304b\u3051\u7b97\u3092\u3059\u308b\u3068\u304d\u3001\u4f59\u308a\u306f\u3069\u306e\u3088\u3046\u306b\u5909\u5316\u3059\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u307e\u305a\u3001\u4ee5\u4e0b\u306e2\u3064\u306e\u5408\u540c\u5f0f\u3092\u8003\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(8\u226111\\) \\((mod\\) \\(3)\\)<\/li>\n<li>\\(4\u22617\\) \\((mod\\) \\(3)\\)<\/li>\n<\/ul>\n<p>\\(8\u226111\\) \\((mod\\) \\(3)\\)\u306f\u4f59\u308a\u304c2\u3067\u3059\u3002\\(4\u22617\\) \\((mod\\) \\(3)\\)\u306f\u4f59\u308a\u304c1\u3067\u3059\u3002\u3044\u305a\u308c\u306b\u3057\u3066\u3082\u3001\u3053\u306e\u3088\u3046\u306a\u5408\u540c\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<p><strong>\u30fb\u5408\u540c\u5f0f\u306e\u8db3\u3057\u7b97<\/strong><\/p>\n<p>\u5272\u308b\u6570\uff08\u4eca\u56de\u306f3\uff09\u304c\u540c\u3058\u5834\u5408\u3001\u5408\u540c\uff08\u2261\uff09\u3067\u7d50\u3070\u308c\u305f\u6570\u5b57\u3092\u8db3\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(8+4\u226111+7\\) \\((mod\\) \\(3)\\)<\/p>\n<p>\\(12\u226118\\) \\((mod\\) \\(3)\\)<\/p>\n<p>\\(12\u226118\\) \\((mod\\) \\(3)\\)\u306e\u4f59\u308a\u306f0\u3067\u3042\u308a\u3001\u5408\u540c\u5f0f\u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p><strong>\u30fb\u5408\u540c\u5f0f\u306e\u5f15\u304d\u7b97<\/strong><\/p>\n<p>\u6b21\u306b\u5f15\u304d\u7b97\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002\u5272\u308b\u6570\\(n\\)\u304c\u540c\u3058\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5f15\u304d\u7b97\u3092\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(8-4\u226111-7\\) \\((mod\\) \\(3)\\)<\/p>\n<p>\\(4\u22614\\) \\((mod\\) \\(3)\\)<\/p>\n<p>\u4e21\u65b9\u3068\u3082\u4f59\u308a\u306f1\u306e\u305f\u3081\u3001\u5408\u540c\u5f0f\u306f\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<p><strong>\u30fb\u5408\u540c\u5f0f\u306e\u304b\u3051\u7b97<\/strong><\/p>\n<p>\u304b\u3051\u7b97\u306b\u3064\u3044\u3066\u3082\u540c\u69d8\u306b\u3001\u5272\u308b\u6570\\(n\\)\u304c\u540c\u3058\u5834\u5408\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u304b\u3051\u7b97\u3092\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(8\u00d74\u226111\u00d77\\) \\((mod\\) \\(3)\\)<\/p>\n<p>\\(32\u226177\\) \\((mod\\) \\(3)\\)<\/p>\n<p>\u4f59\u308a\u306e\u6570\u306f\u4e21\u65b9\u3068\u30822\u306b\u306a\u308b\u305f\u3081\u3001\u5408\u540c\u5f0f\u304c\u6210\u308a\u7acb\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n<p><strong>\u30fb\u8db3\u3057\u7b97\u3001\u5f15\u304d\u7b97\u3001\u304b\u3051\u7b97\u3067\u5408\u540c\u5f0f\u3092\u5229\u7528\u3059\u308b<\/strong><\/p>\n<p>\u305d\u3053\u3067\u3001\u6570\u5f0f\u3092\u5229\u7528\u3057\u3066\u5408\u540c\u5f0f\u306e\u6027\u8cea\u3092\u8868\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e2\u3064\u306e\u5408\u540c\u5f0f\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a\u2261b\\) \\((mod\\)\u00a0\\(n)\\)<\/li>\n<li>\\(c\u2261d\\) \\((mod\\) \\(n)\\)<\/li>\n<\/ul>\n<p>\\(n\\)\u3067\u5272\u308b\u3068\u304d\u3001\\(a\\)\u3068\\(b\\)\u306e\u4f59\u308a\u306f\u540c\u3058\u3067\u3059\u3002\u307e\u305f\u3001\\(n\\)\u3067\u5272\u308b\u3068\u304d\u3001\\(c\\)\u3068\\(d\\)\u306e\u4f59\u308a\u306f\u540c\u3058\u3067\u3059\u3002<\/p>\n<p>\\(a\u2261b\\) \\((mod\\) \\(n)\\)\u3068\\(c\u2261d\\) \\((mod\\) \\(n)\\)\u3092\u6bd4\u8f03\u3059\u308b\u3068\u3001\u4f59\u308a\u306e\u6570\u306f\u7570\u306a\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u305f\u3060\u3044\u305a\u308c\u306b\u3057\u3066\u3082\u3001\\(n\\)\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u4e0a\u8a18\u306e\u5408\u540c\u5f0f\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8db3\u3057\u7b97\u3084\u5f15\u304d\u7b97\u3001\u304b\u3051\u7b97\u3092\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a+c\u2261b+d\\) \\((mod\\) \\(n)\\)<\/li>\n<li>\\(a-c\u2261b-d\\) \\((mod\\) \\(n)\\)<\/li>\n<li>\\(ac\u2261bd\\) \\((mod\\) \\(n)\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3064\u305f\u3081\u3001<span style=\"color: #ff0000;\">\u5408\u540c\u5f0f\u3067\u306f\u81ea\u7531\u306b\u79fb\u9805\u3057\u305f\u308a\u3001\u4e21\u8fba\u3092\u7b49\u500d\u3057\u305f\u308a\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059\u3002<\/span>\u5408\u540c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3068\u304d\u3001\u3053\u306e\u6027\u8cea\u304c\u91cd\u8981\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><strong>\u30fb\u7df4\u7fd2\u554f\u984c<\/strong><\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\\(x\\)\u304c\u6700\u5c0f\u306e\u81ea\u7136\u6570\u3068\u306a\u308b\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306b\u3064\u3044\u3066\\(x\\)\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(x-4\u22617\\) \\((mod\\) \\(3)\\)<\/li>\n<\/ul>\n<p>\u524d\u8ff0\u306e\u901a\u308a\u3001\u5408\u540c\u5f0f\u3067\u306f\u81ea\u7531\u306b\u79fb\u9805\u3057\u305f\u308a\u3001\u4e21\u8fba\u3092\u304b\u3051\u305f\u308a\u3067\u304d\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u79fb\u9805\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(x-4\u22617\\) \\((mod\\) \\(3)\\)<\/p>\n<p>\\(x\u22617+4\\) \\((mod\\) \\(3)\\)<\/p>\n<p>\\(x\u226111\\) \\((mod\\) \\(3)\\)<\/p>\n<p>\u305f\u3060\u3001\\(x\\)\u306f\u6700\u5c0f\u306e\u81ea\u7136\u6570\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5f62\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(x\u226111\u22612\\) \\((mod\\) \\(3)\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(x=2\\)\u304c\u6b63\u89e3\u3067\u3059\u3002<\/p>\n<h3>\u5408\u540c\u5f0f\u306e\u5272\u308a\u7b97\u306f\u4e92\u3044\u306e\u7d20\u306e\u5834\u5408\u306e\u307f\u53ef\u80fd<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u5408\u540c\u5f0f\u306e\u5272\u308a\u7b97\u306f\u3069\u3046\u8003\u3048\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5148\u307b\u3069\u3068\u306f\u7570\u306a\u308a\u3001\u4e21\u8fba\u3092\u81ea\u7531\u306b\u5272\u3063\u3066\u306f\u3044\u3051\u307e\u305b\u3093\u3002<span style=\"color: #0000ff;\">\u308f\u308a\u7b97\u3092\u3059\u308b\u3068\u304d\u3001\u4ee5\u4e0b\u306e\\(a\\)\u3068\\(n\\)\u304c\u4e92\u3044\u306b\u7d20\u306e\u5834\u5408\u306e\u307f\u53ef\u80fd\u3067\u3059\u3002<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/06\/jfhe1.jpg\" alt=\"\" width=\"600\" height=\"105\" class=\"aligncenter size-full wp-image-6854\" \/><\/p>\n<p>\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u5408\u540c\u5f0f\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(14\u22618\\) \\((mod\\) \\(3)\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u5408\u540c\u5f0f\u306b\u3064\u3044\u3066\u30012\u3067\u5272\u308a\u307e\u3057\u3087\u3046\u30022\u30683\uff08mod\uff09\u306f\u4e92\u3044\u306b\u7d20\u3067\u3042\u308b\u305f\u3081\u3001\u5272\u308a\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5316\u3057\u307e\u3059\u3002<\/p>\n<p>\\(14\u00f72\u22618\u00f72\\) \\((mod\\) \\(3)\\)<\/p>\n<p>\\(7\u22614\\) \\((mod\\) \\(3)\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u4f59\u308a\u304c1\u306b\u306a\u308b\u5408\u540c\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u4e00\u65b9\u3001\u4ee5\u4e0b\u306e\u5408\u540c\u5f0f\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(14\u226110\\) \\((mod\\) \\(4)\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u5408\u540c\u5f0f\u306b\u3064\u3044\u30662\u3067\u5272\u308a\u307e\u3057\u3087\u3046\u30022\u30684\u306f\u4e92\u3044\u306b\u7d20\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(14\u00f72\u226110\u00f72\\) \\((mod\\) \\(4)\\)<\/p>\n<p>\\(7\u22615\\) \\((mod\\) \\(4)\\)\uff08\u5408\u540c\u5f0f\u304c\u6210\u7acb\u3057\u306a\u3044\uff09<\/p>\n<p>7\u30924\u3067\u5272\u308b\u3068\u3001\u4f59\u308a\u306f3\u3067\u3059\u3002\u4e00\u65b9\u30015\u30924\u3067\u5272\u308b\u3068\u4f59\u308a\u306f1\u3067\u3059\u3002\u3053\u3046\u3057\u3066\u3001\u5408\u540c\u5f0f\u304c\u6210\u7acb\u3057\u307e\u305b\u3093\u3002\u5408\u540c\u5f0f\u3092\u5229\u7528\u3057\u3066\u5272\u308a\u7b97\u3092\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u4e92\u3044\u306b\u7d20\u306e\u95a2\u4fc2\u3092\u5229\u7528\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n<p><strong>\u30fb\u7df4\u7fd2\u554f\u984c<\/strong><\/p>\n<p>\u305d\u308c\u3067\u306f\\(x\\)\u304c\u6700\u5c0f\u306e\u81ea\u7136\u6570\u3068\u306a\u308b\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306b\u3064\u3044\u3066\\(x\\)\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(3x\u226113\\) \\((mod\\) \\(5)\\)<\/li>\n<\/ul>\n<p>\\(a-b\\)\u304c5\u306e\u500d\u6570\u306b\u306a\u308c\u3070\u3044\u3044\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(3x-13=5\\)<\/p>\n<p>\\(3x=18\\)<\/p>\n<p>\u3064\u307e\u308a\u3001\u4ee5\u4e0b\u306e\u5f0f\u3078\u5909\u5f62\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(3x\u226118\\) \\((mod\\) \\(5)\\)<\/p>\n<p>\\(3x\u22613\u00d76\\) \\((mod\\) \\(5)\\)<\/p>\n<p>3\u30685\u306f\u4e92\u3044\u306b\u7d20\u306a\u306e\u3067\u3001\u5272\u308a\u7b97\u3092\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u4ee5\u4e0b\u306e\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(x\u22616\\) \\((mod\\) \\(5)\\)<\/p>\n<p>\u305f\u3060\\(x\\)\u306f\u6700\u5c0f\u306e\u81ea\u7136\u6570\u306a\u306e\u3067\u3001\u4ee5\u4e0b\u306e\u5408\u540c\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(x\u22616\u22611\\) \\((mod\\) \\(5)\\)<\/p>\n<p>\u6cd5\u304c5\u3067\u3042\u308b\u305f\u3081\u30015\u306e\u500d\u6570\u3092\u5229\u7528\u3057\u3066\u5f15\u304d\u7b97\uff08\u307e\u305f\u306f\u8db3\u3057\u7b97\uff09\u3092\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305d\u3053\u3067\\(6-5=1\\)\u306b\u306a\u308a\u3001\\(x=1\\)\u304c\u7b54\u3048\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<h3>\u3079\u304d\u4e57\uff08\u7d2f\u4e57\uff09\u3067\u306e\u5408\u540c\u5f0f\u306e\u8a08\u7b97\u65b9\u6cd5<\/h3>\n<p>\u6b21\u306b\u3079\u304d\u4e57\uff08\u7d2f\u4e57\uff09\u3067\u306e\u5408\u540c\u5f0f\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002\u6307\u6570\u3092\u542b\u3080\u5408\u540c\u5f0f\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u5408\u540c\u5f0f\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(4\u22617\\) \\((mod\\) \\(3)\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4e8c\u4e57\u3084\u4e09\u4e57\u3092\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><strong>\u30fb\u4e8c\u4e57\u3092\u884c\u3046<\/strong><\/p>\n<p>\\(4^2\u22617^2\\) \\((mod\\) \\(3)\\)<\/p>\n<p>\\(16\u226149\\) \\((mod\\) \\(3)\\)<\/p>\n<p><strong>\u30fb\u4e09\u4e57\u3092\u884c\u3046<\/strong><\/p>\n<p>\\(4^3\u22617^3\\) \\((mod\\) \\(3)\\)<\/p>\n<p>\\(64\u2261343\\) \\((mod\\) \\(3)\\)<\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u78ba\u8a8d\u3059\u308b\u3068\u3001\\(a-b\\)\u306b\u3088\u3063\u30663\u306e\u500d\u6570\u3092\u4f5c\u308c\u307e\u3059\u3002\u3064\u307e\u308a<span style=\"color: #ff0000;\">\u6307\u6570\u3092\u542b\u3080\u5408\u540c\u5f0f\u306b\u3064\u3044\u3066\u3001\u7d2f\u4e57\u3092\u3057\u3066\u3082\u4f59\u308a\u306f\u5909\u5316\u3057\u307e\u305b\u3093\u3002<\/span>\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/06\/jfhe2.jpg\" alt=\"\" width=\"600\" height=\"46\" class=\"aligncenter size-full wp-image-6855\" \/><\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u5171\u901a\u3059\u308b\u6307\u6570\u3092\u5229\u7528\u3059\u308c\u3070\u3001\u5408\u540c\u5f0f\u3067\u306f\u6307\u6570\u3092\u53d6\u308a\u5916\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p><strong>\u30fb\u7df4\u7fd2\u554f\u984c\uff1a\u3079\u304d\u4e57\u3067\u306e\u4f59\u308a\u3092\u6c42\u3081\u308b<\/strong><\/p>\n<p>\u305d\u308c\u3067\u306f\\(x\\)\u304c\u6700\u5c0f\u306e\u81ea\u7136\u6570\u3068\u306a\u308b\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(13^{100}\\)\u30924\u3067\u5272\u3063\u305f\u3068\u304d\u306e\u4f59\u308a\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>13\u306e100\u4e57\u3092\u8a08\u7b97\u3057\u3066\u306f\u3044\u3051\u307e\u305b\u3093\u3002\u305d\u3046\u3067\u306f\u306a\u304f\u3001\u4ee5\u4e0b\u306e\u5408\u540c\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u3092\u8003\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(13^{100}\u2261b^{100}\\) \\((mod\\) \\(4)\\)<\/p>\n<p>\u3053\u306e\u5408\u540c\u5f0f\u3092\u4f5c\u308c\u3070\u3001100\u4e57\u3092\u53d6\u308a\u5916\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u7d50\u679c\u3001\u4f59\u308a\u306e\u8a08\u7b97\u304c\u697d\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>100\u4e57\u3092\u53d6\u308a\u5916\u3057\u3066\\(13\u2261b\\) \\((mod\\) \\(4)\\)\u3092\u4f5c\u308b\u3068\u304d\u3001\\(13-b\\)\u304c4\u306e\u500d\u6570\u306b\u306a\u308c\u3070\u3044\u3044\u3067\u3059\u3002\u305d\u3053\u30674\u306e\u500d\u6570\u3067\u3042\u308b12\u3092\u5229\u7528\u3057\u3001\\(13-12=1\\)\u306b\u3088\u3063\u3066\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(13\u22611\\) \\((mod\\) \\(4)\\)<\/p>\n<p><span style=\"color: #0000ff;\">\u7d2f\u4e57\u3092\u542b\u3080\u5408\u540c\u5f0f\u306e\u8a08\u7b97\u554f\u984c\u3067\u306f\u3001\u5408\u540c\u5f0f\u306b\u542b\u307e\u308c\u308b\u5024\uff08\u4eca\u56de\u306e\u4f8b\u3067\u306f\\(b\\)\uff09\u304c\u6700\u3082\u5c0f\u3055\u3044\u81ea\u7136\u6570\u3068\u306a\u308b\u3088\u3046\u306b\u8a2d\u5b9a\u3057\u3001\u65b0\u305f\u306a\u5408\u540c\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/span>\u305d\u3046\u3059\u308c\u3070\u3001\u8a08\u7b97\u304c\u7c21\u5358\u306b\u306a\u308a\u307e\u3059\u3002\u5148\u307b\u3069\u306e\u5f0f\u3067\u306f\u3001\u6700\u3082\u5c0f\u3055\u3044\u81ea\u7136\u6570\u306f1\u306a\u306e\u3067\\(13\u22611\\) \\((mod\\) \\(4)\\)\u3068\u3057\u307e\u3059\u3002<\/p>\n<p>\u6b21\u306b\u3001\u4e21\u8fba\u3092100\u4e57\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(13^{100}\u22611^{100}\\) \\((mod\\) \\(4)\\)<\/p>\n<p>\u91cd\u8981\u306a\u306e\u306f\u3001\\(1^{100}=1\\)\u3067\u3042\u308b\u3053\u3068\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u5408\u540c\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<p>\\(13^{100}\u22611^{100}\u22611\\) \\((mod\\) \\(4)\\)<\/p>\n<p>1\u306b\u7740\u76ee\u3059\u308b\u3068\u30014\u3067\u5272\u308b\u3068\u304d\u306e\u4f59\u308a\u306f1\u3067\u3059\u3002\u3064\u307e\u308a\u3001\\(13^{100}\\)\u30924\u3067\u5272\u3063\u305f\u3068\u304d\u306e\u4f59\u308a\u306f1\u3067\u3059\u3002<\/p>\n<p><strong>\u30fb\u7df4\u7fd2\u554f\u984c\uff1a1\u306e\u4f4d\u3092\u6c42\u3081\u308b<\/strong><\/p>\n<p>\u306a\u304a\u5408\u540c\u5f0f\u306e\u8a08\u7b97\u3067\u306f\u30011\u306e\u4f4d\u3092\u6c42\u3081\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u30b1\u30fc\u30b9\u3082\u3042\u308a\u307e\u3059\u3002\u81ea\u7136\u6570\u306e1\u306e\u4f4d\u3092\u6c42\u3081\u308b\u3068\u3044\u3046\u306e\u306f\u300110\u3067\u5272\u308b\u3068\u304d\u306e\u4f59\u308a\u3092\u51fa\u3059\u306e\u3068\u610f\u5473\u304c\u540c\u3058\u3067\u3059\u3002\u4f8b\u3048\u307023\u309210\u3067\u308f\u308b\u3068\u3001\u4f59\u308a\u306f3\u3067\u3059\u3002736\u309210\u3067\u308f\u308b\u3068\u3001\u4f59\u308a\u306f6\u3067\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u300110\u3067\u5272\u308c\u30701\u306e\u4f4d\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(13^{101}\\)\u306b\u3064\u3044\u3066\u30011\u306e\u4f4d\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u307e\u305a\u3001\u5408\u540c\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002\u6cd5\u306f10\u306a\u306e\u3067\u3001\u4ee5\u4e0b\u306e\u5408\u540c\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<p>\\(13\u22613\\) \\((mod\\) \\(10)\\)<\/p>\n<p>\u3064\u307e\u308a\u3001\\(13^{101}\u22613^{101}\\) \\((mod\\) \\(10)\\)\u3092\u4f5c\u308c\u3070\u3044\u3044\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u305d\u3053\u30673\u306b\u7740\u76ee\u3057\u3066\u3001\u6307\u6570\u3092\u542b\u3080\u4ee5\u4e0b\u306e\u5408\u540c\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(3^2\u22619\\) \\((mod\\) \\(10)\\)<\/li>\n<li>\\(3^3\u226127\u22617\\) \\((mod\\) \\(10)\\)<\/li>\n<li>\\(3^4\u226181\u22611\\) \\((mod\\) \\(10)\\)<\/li>\n<\/ul>\n<p>\u3079\u304d\u4e57\u306e\u8a08\u7b97\u306b\u3088\u308a\u3001\\(3^4\u22611\\) \\((mod\\) \\(10)\\)\u306e\u5408\u540c\u5f0f\u3092\u767a\u898b\u3057\u305f\u305f\u3081\u3001\u3053\u308c\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u554f\u984c\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/06\/jfhe4.jpg\" alt=\"\" width=\"543\" height=\"254\" class=\"aligncenter size-full wp-image-6857\" \/><\/p>\n<p>\u305d\u3053\u30673\u306b\u7740\u76ee\u3059\u308b\u3068\u30013\u309210\u3067\u5272\u308b\u3068\u304d\u306e\u4f59\u308a\u306f3\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(13^{101}\\)\u306e1\u306e\u4f4d\u306f3\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<h2>\u6574\u6570\u306e\u5272\u308a\u7b97\u3067\u6570\u5f0f\u306e\u4ee3\u308f\u308a\u306b\u5408\u540c\u5f0f\u3092\u4f7f\u3063\u3066\u8a3c\u660e\u3059\u308b<\/h2>\n<p>\u305d\u308c\u3067\u306f\u3001\u306a\u305c\u5408\u540c\u5f0f\u3092\u5b66\u3076\u5fc5\u8981\u304c\u3042\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5408\u540c\u5f0f\u3092\u5229\u7528\u3059\u308b\u5834\u5408\u3001\u5272\u308a\u7b97\u3067\u306e\u4f59\u308a\u3084\u500d\u6570\u304c\u95a2\u308f\u308b\u554f\u984c\u3092\u89e3\u304f\u306e\u304c\u975e\u5e38\u306b\u7c21\u5358\u306b\u306a\u308a\u307e\u3059\u3002\u8907\u96d1\u306a\u8a08\u7b97\u3092\u3057\u306a\u304f\u3066\u3082\u3001\u6574\u6570\u306e\u5272\u308a\u7b97\u3084\u500d\u6570\u306e\u8a3c\u660e\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u6574\u6570\u306e\u5272\u308a\u7b97\u3084\u500d\u6570\u306e\u8a3c\u660e\u554f\u984c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u6570\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u554f\u984c\u3092\u89e3\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a=bq+r\\)<\/li>\n<\/ul>\n<p>\u305f\u3060\u3001\u7279\u306b\u7d2f\u4e57\u3092\u542b\u3080\u5f0f\u3067\u306f\u8a08\u7b97\u304c\u5927\u5909\u3067\u3059\u3002\u305d\u3053\u3067\u5408\u540c\u5f0f\u3092\u5229\u7528\u3059\u308c\u3070\u3001\u9762\u5012\u306a\u8a08\u7b97\u306a\u3057\u306b\u6574\u6570\u306e\u5272\u308a\u7b97\u3084\u500d\u6570\u306e\u8a3c\u660e\u554f\u984c\u3092\u89e3\u3051\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u4f8b\u3068\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u8a3c\u660e\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(n^4+2n^2\\)\u304c3\u306e\u500d\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u3053\u3053\u3067\u306f\u5408\u540c\u5f0f\u3092\u5229\u7528\u3057\u3066\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002\u307e\u305a\u30013\u306e\u500d\u6570\u306a\u306e\u3067\u4f59\u308a\u306f0\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3059\u3079\u3066\u306e\u6574\u6570\u306b\u3064\u3044\u3066\u3001\\(n^4+2n^2\\)\u306e\u4f59\u308a\u304c0\u3067\u3042\u308b\u3068\u8a3c\u660e\u3059\u308c\u3070\u3044\u3044\u3067\u3059\u3002<\/p>\n<p>\u307e\u305f<span style=\"color: #0000ff;\">\u500d\u6570\u306e\u3088\u3046\u306b\u6cd5\u304c\u56fa\u5b9a\u3055\u308c\u308b\u5834\u5408\u3001\u4f59\u308a\u306f\u6cd5\u3092\u57fa\u6e96\u306b\u3057\u305f\u898f\u5247\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/span>\u4f8b\u3048\u30703\u306e\u500d\u6570\uff08\u6cd5\u304c3\uff09\u306e\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b3\u304c\u52a0\u308f\u308b\u3054\u3068\u306b\u4f59\u308a\u304c\u540c\u3058\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(1\u22614\u22617\\) \\((mod\\) \\(3)\\)\uff1a\u4f59\u308a1<\/li>\n<li>\\(2\u22615\u22618\\) \\((mod\\) \\(3)\\)\uff1a\u4f59\u308a2<\/li>\n<li>\\(3\u22616\u22619\\) \\((mod\\) \\(3)\\)\uff1a\u4f59\u308a0<\/li>\n<\/ul>\n<p>\u6cd5\u5247\u6027\u304c\u3042\u308b\u3053\u3068\u306b\u3064\u3044\u3066\u306f\u3001\u5408\u540c\u5f0f\u3092\u4f5c\u308b\u3068\u304d\u306b\u300c\\(a-b\\)\u304c3\u306e\u500d\u6570\u306b\u306a\u308b\u304b\u3069\u3046\u304b\u300d\u3092\u8abf\u3079\u308c\u3070\u3044\u3044\u3053\u3068\u304b\u3089\u3082\u308f\u304b\u308a\u307e\u3059\u3002\u3064\u307e\u308a\\(n^4+2n^2\\)\u304c3\u306e\u500d\u6570\u304b\u3069\u3046\u304b\u8abf\u3079\u308b\u305f\u3081\u306b\u306f\u3001\u4efb\u610f\u306e\u6574\u6570\\(k\\)\u306b\u3064\u3044\u3066\u3001\u4ee5\u4e0b\u306e\u30b1\u30fc\u30b9\u306e\u4f59\u308a\u304c\u3069\u306e\u3088\u3046\u306b\u306a\u308b\u306e\u304b\u8abf\u3079\u308c\u3070\u3044\u3044\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(k\\) \\((mod\\) \\(3)\\)<\/li>\n<li>\\(k+1\\) \\((mod\\) \\(3)\\)<\/li>\n<li>\\(k+2\\) \\((mod\\) \\(3)\\)<\/li>\n<\/ul>\n<p>\\(k\\)\u306f\u3069\u306e\u5024\u3067\u3042\u3063\u3066\u3082\u554f\u984c\u3042\u308a\u307e\u305b\u3093\u3002\u8a08\u7b97\u3057\u3084\u3059\u3044\u5024\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002\u305d\u3053\u3067\u3001\\(k=1\\)\u306e\u3068\u304d\u306e\u4f59\u308a\u3092\u8abf\u3079\u307e\u3057\u3087\u3046\u3002\u3064\u307e\u308a\\(n\\)\u304c1\u307e\u305f\u306f2\u307e\u305f\u306f3\u306e\u3068\u304d\u3001\u4f59\u308a\u3092\u8abf\u3079\u307e\u3059\u3002<\/p>\n<p><strong>\u30fb\\(n=1\\)\u306e\u3068\u304d<\/strong><\/p>\n<p>\\(n^4\\)\u3092\u8abf\u3079\u307e\u3057\u3087\u3046\u3002\\(1^4=1\\)\u3067\u3042\u308a\u3001\\(1\\) \\((mod\\) \\(3)\\)\u306e\u4f59\u308a\u306f1\u3067\u3059\u3002\u6b21\u306b\\(2n^2\\)\u3092\u8abf\u3079\u307e\u3057\u3087\u3046\u3002\\(2\u00d71^2=2\\)\u3067\u3042\u308a\u3001\\(2\\) \\((mod\\) \\(3)\\)\u306e\u4f59\u308a\u306f2\u3067\u3059\u3002\u305d\u306e\u305f\u3081\\(n^4+2n^2\\)\u306e\u4f59\u308a\u306f0\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><strong>\u30fb\\(n=2\\)\u306e\u3068\u304d<\/strong><\/p>\n<p>\\(n^4\\)\u306b\u3064\u3044\u3066\u3001\\(2^4=16\\)\u3067\u3042\u308a\u3001\\(16\\) \\((mod\\) \\(3)\\)\u306e\u4f59\u308a\u306f1\u3067\u3059\u3002\u307e\u305f\\(2n^2\\)\u306b\u3064\u3044\u3066\u3001\\(2\u00d72^2=8\\)\u3067\u3059\u3002\\(8\\) \\((mod\\) \\(3)\\)\u306e\u4f59\u308a\u306f2\u3067\u3059\u3002\u305d\u306e\u305f\u3081\\(n^4+2n^2\\)\u306e\u4f59\u308a\u306f0\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><strong>\u30fb\\(n=3\\)\u306e\u3068\u304d<\/strong><\/p>\n<p>\\(n^4\\)\u306b3\u3092\u4ee3\u5165\u3059\u308b\u3068\u3001\\(3^4=81\\)\u3068\u306a\u308a\u3001\\(81\\) \\((mod\\) \\(3)\\)\u306e\u4f59\u308a\u306f0\u3067\u3059\u3002\\(2n^2\\)\u306b\u3064\u3044\u3066\u306f\u3001\\(2\u00d73^2=18\\)\u3068\u306a\u308a\u3001\\(18\\) \\((mod\\) 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