{"id":39006,"date":"2023-11-21T19:34:07","date_gmt":"2023-11-21T19:34:07","guid":{"rendered":"https:\/\/science-hub.click\/%E3%83%95%E3%82%A7%E3%83%AB%E3%83%9E%E3%83%BC%E3%81%AE%E6%9C%80%E7%B5%82%E5%AE%9A%E7%90%86-%E5%AE%9A%E7%BE%A9\/"},"modified":"2023-11-21T19:34:07","modified_gmt":"2023-11-21T19:34:07","slug":"%E3%83%95%E3%82%A7%E3%83%AB%E3%83%9E%E3%83%BC%E3%81%AE%E6%9C%80%E7%B5%82%E5%AE%9A%E7%90%86-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=39006","title":{"rendered":"\u30d5\u30a7\u30eb\u30de\u30fc\u306e\u6700\u7d42\u5b9a\u7406 – \u5b9a\u7fa9"},"content":{"rendered":"

\u5c0e\u5165<\/h2>
\n\"\"<\/figure>
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\n\"\"<\/figure>
\u30a2\u30f3\u30c9\u30ea\u30e5\u30fc\u30fb\u30ef\u30a4\u30eb\u30ba<\/div><\/div><\/div>

\u6570\u5b66<\/a><\/span>\u306b\u304a\u3051\u308b\u30d5\u30a7\u30eb\u30de\u30fc\u306e\u6700\u7d42\u5b9a\u7406<\/b>\u3001\u307e\u305f\u306f\u30d5\u30a7\u30eb\u30de\u30fc\u30fb\u30ef\u30a4\u30eb\u30ba\u306e\u5b9a\u7406\u306f<\/b>\u3001\u6b21\u306e\u3088\u3046\u306b\u8ff0\u3079\u3089\u308c\u308b\u6570\u8ad6<\/a><\/span>\u306e\u5b9a\u7406\u3067\u3059\u3002<\/p>

\u5b9a\u7406<\/strong>\u2014<\/span>\u6b21\u306e\u3088\u3046\u306a\u30bc\u30ed\u4ee5\u5916\u306e\u6574\u6570x<\/i><\/span> \u3001 y<\/i><\/span> \u3001 z \u306f<\/i><\/span>\u5b58\u5728\u3057\u307e\u305b\u3093\u3002 <\/p>

$$ {x^n+y^n=z^n \\,} $$<\/div><\/center><\/dd><\/dl>

n \u304c<\/i><\/span>\u53b3\u5bc6\u306b2<\/i>\u3088\u308a\u5927\u304d\u3044\u6574\u6570\u306b\u306a\u308b\u3068\u3059\u3050\u306b\u3002<\/p><\/div>

\u3053\u306e\u5b9a\u7406\u306e\u540d\u524d\u306f\u3001\u30c7\u30a3\u30aa\u30d5\u30a1\u30f3\u30c8\u30b9\u306e\u300e Arithmetica\u300f<\/i>\u306e\u7ffb\u8a33\u306e\u6b04\u5916\u306b\u3001\u3053\u306e\u554f\u984c\u306e\u8a18\u8ff0\u306b\u7d9a\u3044\u3066\u6b21\u306e\u3088\u3046\u306b\u66f8\u3044\u305f\u30d4\u30a8\u30fc\u30eb\u30fb\u30c9\u30fb\u30d5\u30a7\u30eb\u30de\u30fc\u306b\u7531\u6765\u3057\u3066\u3044\u307e\u3059\u3002<\/p>

\u300c…\u79c1\u306f\u3053\u306e\u547d\u984c\u306e\u7d20\u6674\u3089\u3057\u3044\u5b9f\u8a3c\u3092\u898b\u3064\u3051\u307e\u3057\u305f\u304c\u3001\u305d\u308c\u3092\u53ce\u3081\u308b\u306b\u306f\u4f59\u767d\u304c\u72ed\u3059\u304e\u307e\u3059\u3002 \u00bb<\/div><\/blockquote>

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\u4eca\u65e5\u3001\u307b\u3068\u3093\u3069\u306e\u6570\u5b66\u8005\u306f\u3001\u30d5\u30a7\u30eb\u30de\u30fc\u304c\u81ea\u5206\u306e\u4e88\u60f3\u3092\u8a3c\u660e\u3057\u305f\u3068\u4fe1\u3058\u305f\u306e\u306f\u304a\u305d\u3089\u304f\u9593\u9055\u3044\u3060\u3063\u305f\u3068\u4fe1\u3058\u3066\u3044\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u5f7c\u304c\u5f53\u6642\u306e\u6570\u5b66\u306e\u307f\u3092\u4f7f\u7528\u3057\u3066\u65b9\u6cd5\u3092\u767a\u898b\u3057\u305f\u3068\u8003\u3048\u308b\u3053\u3068\u3092\u59a8\u3052\u308b\u3082\u306e\u306f\u4f55\u3082\u3042\u308a\u307e\u305b\u3093\u3002\u78ba\u304b\u306b\u3001\u3053\u306e\u7a2e\u306e\u65b9\u6cd5\u304c\u5b58\u5728\u3059\u308b\u3068\u3044\u3046\u5e0c\u671b\u306f\u307b\u3068\u3093\u3069\u3042\u308a\u307e\u305b\u3093\u3002\u3057\u304b\u3057\u3001\u3044\u3064\u304b\u767a\u898b\u3067\u304d\u308b\u306e\u3067\u306f\u306a\u3044\u304b<\/a><\/span>\u3068\u671f\u5f85\u3057\u7d9a\u3051\u308b\u4eba\u3082\u3044\u307e\u3059\u3002<\/p>

\n\"\u30d5\u30a7\u30eb\u30de\u30fc\u306e\u6700\u7d42\u5b9a\u7406<\/figure>

\u5b9f\u8a3c\u65b9\u6cd5<\/h2>

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  1. \u30d5\u30a7\u30eb\u30de\u30fc\u65b9\u7a0b\u5f0f<\/a><\/span>\u306e\u89e3\u3092\u7279\u5b9a\u306e\u6955\u5186\u66f2\u7dda<\/a><\/span>\u306b\u95a2\u9023\u4ed8\u3051\u307e\u3059 (Frey\u3001Helleguearch \u304b\u3089\u30a2\u30a4\u30c7\u30a2\u3092\u63a1\u7528)\u3001<\/li>
  2. Frey-Hellegouarch\u66f2\u7dda\u306f<\/a><\/span>\u30e2\u30b8\u30e5\u30e9\u30fc\u95a2\u6570\u3067\u30d1\u30e9\u30e1\u30fc\u30bf\u5316\u3067\u304d\u306a\u3044\u3053\u3068\u3092\u5b9f\u8a3c\u3057\u307e\u3059 (Ribet\u3001\u30bb\u30fc\u30eb\u4e88\u60f3\u3092\u5b9f\u8a3c)\u3002<\/li>
  3. \u4efb\u610f\u306e\u6955\u5186\u66f2\u7dda\u3001\u307e\u305f\u306f\u30d5\u30ec\u30a4\u30fb\u30d8\u30eb\u30b0\u30a2\u30eb\u30af\u306e\u6955\u5186\u66f2\u7dda\u3092\u542b\u3080\u306e\u306b\u5341\u5206\u306a\u5927\u304d\u3055\u306e\u30af\u30e9\u30b9\u304c\u30e2\u30b8\u30e5\u30e9\u30fc\u95a2\u6570\u306b\u3088\u3063\u3066\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u5316\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u5fd7\u6751\u30fb\u8c37\u5c71\u30fb\u30f4\u30a7\u30a4\u30e6\u4e88\u60f3\u3067\u3042\u308a\u3001\u6570\u8ad6\u306b\u304a\u3044\u3066\u975e\u5e38\u306b\u91cd\u8981\u3067\u3059\u3002<\/li><\/ol>

    \u7d50\u679c\u3068\u3057\u3066\u751f\u3058\u308b\u77db\u76fe\u306f<\/a><\/span>\u3001\u30d5\u30a7\u30eb\u30de\u30fc\u306e\u65b9\u7a0b\u5f0f\u304c\u89e3\u3092\u6301\u305f\u306a\u3044\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/p>

    \u6955\u5186\u66f2\u7dda<\/span><\/h3>

    \u6955\u5186\u66f2\u7dda\u306f\u3001\u6b21\u306e\u5f62\u5f0f\u306e\u65b9\u7a0b\u5f0f\u66f2\u7dda\u3067\u3059\u3002<\/p>

    y<\/i> 2<\/sup> + a<\/i> x<\/i> y<\/i> + b<\/i> y<\/i> = x<\/i> 3<\/sup> + c<\/i> x<\/i> 2<\/sup> + d<\/i> x<\/i> + e<\/i><\/span><\/dd><\/dl>

    \u4fc2\u6570 a\u3001b\u3001c\u3001d\u3001\u304a\u3088\u3073 e \u306f\u3001\u66f2\u7dda\u304c\u5b9a\u7fa9\u3055\u308c\u308b\u30dc\u30c7\u30a3\u306e\u8981\u7d20\u3067\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u66f2\u7dda\u304c\u5b9f\u969b\u306b\u6955\u5186\u66f2\u7dda\u3067\u3042\u308b\u305f\u3081\u306b\u306f\u3001\u3053\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u305f\u66f2\u7dda\u304c\u7279\u7570\u3067\u3042\u3063\u3066\u306f\u306a\u308a\u307e\u305b\u3093\u3002\u3064\u307e\u308a\u3001\u5c16\u70b9<\/a><\/span>\u3082\u4e8c\u91cd\u70b9<\/span>\u3082\u6301\u305f\u306a\u3044\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u6700\u5f8c\u306e\u6761\u4ef6\u306f\u3001\u5224\u5225<\/a><\/span>\u5f0f\u306b\u4f3c\u305f\u4fc2\u6570\u4e0a\u306e\u7279\u5b9a\u306e\u591a\u9805\u5f0f<\/a><\/span>\u304c\u30ad\u30e3\u30f3\u30bb\u30eb\u3055\u308c\u306a\u3044\u3068\u3044\u3046\u4e8b\u5b9f\u306b\u3088\u3063\u3066\u8868\u3055\u308c\u307e\u3059\u3002<\/p>

    \u5b9f\u6570\u4f53\u306e\u4f8b\u3092\u53d6\u308b\u3068\u3001\u5b9f\u6570\u4f53\u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u305f\u6955\u5186\u66f2\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f\u3001\u3088\u308a\u5358\u7d14\u306a\u5f62\u5f0f (\u30ef\u30a4\u30a8\u30eb\u30b7\u30e5\u30c8\u30e9\u30b9\u65b9\u7a0b\u5f0f\u3068\u547c\u3070\u308c\u307e\u3059) \u306b\u307e\u3068\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>

    y<\/i> 2<\/sup> = x<\/i> 3<\/sup> + a<\/i> x<\/i> + b<\/i><\/span> \u3002<\/dd><\/dl>

    \u3053\u306e\u66f2\u7dda\u306e\u5224\u5225\u5f0f\u306f\u03b4 = \u2212 16(4 a<\/i> 3<\/sup> + 27 b<\/i> 2<\/sup> )<\/span>\u3067\u3059\u3002\u30bc\u30ed\u4ee5\u5916\u306e\u5834\u5408\u3001\u66f2\u7dda\u306f\u7279\u7570\u3067\u306f\u306a\u3044\u305f\u3081\u3001\u771f\u306e\u6955\u5186\u66f2\u7dda\u306b\u306a\u308a\u307e\u3059\u3002<\/p>

    \u30d5\u30ec\u30a4\u30fb\u30a8\u30eb\u30b0\u30a2\u30eb\u30af\u66f2\u7dda<\/span><\/h3>

    1984 \u5e74\u306b\u3001\u30b2\u30eb\u30cf\u30eb\u30c8 \u30d5\u30e9\u30a4\u306f<\/span>\u3001\u30a4\u30f4 \u30d8\u30eb\u30b0\u30a2\u30eb\u30af\u306e\u53e4\u3044\u30a2\u30a4\u30c7\u30a2\u3092\u53d6\u308a\u4e0a\u3052\u3001 n<\/i> > 2<\/span>\u306e\u30d5\u30a7\u30eb\u30de\u30fc\u65b9\u7a0b\u5f0f\u306e\u89e3\u306b\u3088\u308a\u3001\u5947\u5999\u306a\u7279\u6027\u3092\u6301\u3064\u534a\u5b89\u5b9a\u6955\u5186\u66f2\u7dda\u3092\u5b9a\u7fa9\u3067\u304d\u308b\u3053\u3068\u3092\u5b9f\u8a3c\u3057\u307e\u3057\u305f\u3002\u3053\u308c\u3089\u306f\u65b9\u7a0b\u5f0f\u66f2\u7dda\u3067\u3059\u3002<\/p>

    y<\/i> 2<\/sup> = x<\/i> ( x<\/i> + A<\/i> n<\/i><\/sup> )( x<\/i> \u2212 B<\/i> n<\/i><\/sup> )<\/span> \u3001<\/dd><\/dl>

    \u3053\u3053\u3067\u3001 A<\/i> n<\/i><\/sup> + B<\/i> n<\/i><\/sup> = C<\/i> n \u306f<\/i><\/sup><\/span>\u30d5\u30a7\u30eb\u30de\u30fc\u306e\u5b9a\u7406\u306e\u53cd\u4f8b\u3067\u3059\u3002<\/p>

    \u7d50\u8ad6\u3068\u3057\u3066\u3001\u3053\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u305f\u6955\u5186\u66f2\u7dda\u306b\u306f\u3001\u5b58\u5728\u3059\u308b\u306b\u306f\u5947\u5999\u3059\u304e\u308b\u7279\u6027\u304c\u3042\u308b\u3053\u3068\u3092\u793a\u3059\u3060\u3051\u3067\u5341\u5206\u3067\u3059\u3002<\/p>

    \u6570\u5b66\u306e\u4ed6\u306e\u72b6\u6cc1\u3068\u540c\u69d8\u306b\u3001\u30d5\u30a7\u30eb\u30de\u30fc\u306e\u554f\u984c\u3092\u660e\u3089\u304b\u306b\u306f\u308b\u304b\u306b\u96e3\u3057\u3044\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u306b\u7d71\u5408\u3059\u308b\u3068\u3044\u3046\u4e8b\u5b9f\u306f\u3001\u4f9d\u7136\u3068\u3057\u3066\u9032\u6b69\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u306a\u305c\u306a\u3089\u3001\u3053\u306e\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u7528\u306b\u958b\u767a\u3055\u308c\u305f\u30c4\u30fc\u30eb\u304c\u3059\u3079\u3066<\/a><\/span>\u63c3\u3063\u3066\u3044\u308b\u304b\u3089\u3067\u3059\u3002<\/p>

    \u30b1\u30cd\u30b9\u30fb\u30ea\u30d9\u30c3\u30c8\u6c0f\u306e\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3<\/span><\/h3>

    1986 \u5e74\u3001\u307b\u307c 2 \u5e74\u9593\u306e\u52aa\u529b\u306e\u5f8c\u3001\u30a2\u30e1\u30ea\u30ab\u4eba\u306eKenneth Ribet \u306f<\/span>\u3001Jean-Pierre Serre<\/a><\/span>\u306e\u30a4\u30d7\u30b7\u30ed\u30f3\u4e88\u60f3\u306e\u5927\u90e8\u5206\u3092\u5b9f\u8a3c\u3059\u308b\u3053\u3068\u306b\u6210\u529f\u3057\u307e\u3057\u305f\u3002\u305d\u306e\u7d50\u679c\u306e 1 \u3064\u306f\u3001Frey-Hellegouarch \u66f2\u7dda\u304c\u30e2\u30b8\u30e5\u30e9\u30fc\u95a2\u6570\u3067\u30d1\u30e9\u30e1\u30fc\u30bf\u5316\u3067\u304d\u306a\u3044\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002<\/p>

    \u6b8b\u3063\u3066\u3044\u308b\u306e\u306f\u3001\u300c\u3069\u3093\u306a\u6955\u5186\u66f2\u7dda\u3082\u30e2\u30b8\u30e5\u30e9\u30fc\u95a2\u6570\u3067\u30d1\u30e9\u30e1\u30fc\u30bf\u5316\u3067\u304d\u308b\u300d\u3068\u3044\u3046\u5fd7\u6751\u30fb\u8c37\u5c71\u30fb\u30f4\u30a7\u30a4\u30e6\u4e88\u60f3\u3092\u5b9f\u8a3c\u3059\u308b\u3053\u3068\u3060\u3051\u3060\u3063\u305f\u3002<\/p>

    \u5fd7\u6751\u30fb\u8c37\u5c71\u30fb\u30f4\u30a7\u30a4\u30e6\u4e88\u60f3<\/span><\/h3>

    \u5fd7\u6751\u30fb\u8c37\u5c71\u30fb\u30f4\u30a7\u30a4\u30e6\u4e88\u60f3\u306f\u3001\u6955\u5186\u66f2\u7dda\u304c\u7279\u5225\u306a\u3044\u308f\u3086\u308b\u30e2\u30b8\u30e5\u30e9\u30fc\u95a2\u6570\uff08\u4e09\u89d2\u95a2\u6570\u306e\u4e00\u822c\u5316\uff09\u3068\u5e38\u306b\u95a2\u9023\u4ed8\u3051\u3089\u308c\u308b\uff08\u307e\u305f\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\u5316\u307e\u305f\u306f\u5c0e\u51fa\u3055\u308c\u308b\uff09\u3053\u3068\u304c\u3067\u304d\u308b\u3053\u3068\u3092\u6307\u5b9a\u3057\u307e\u3059\u3002<\/p>

    \u3053\u306e\u4e88\u60f3\u3092\u5b9f\u8a3c\u3059\u308b\u305f\u3081\u306b\u3001\u30a2\u30f3\u30c9\u30ea\u30e5\u30fc \u30ef\u30a4\u30eb\u30ba\u306f\u6b21\u306e\u6570\u5b66\u7684\u6982\u5ff5\u3092\u4f7f\u7528\u3057\u307e\u3057\u305f\u3002<\/p>

n<\/i><\/span>\u306e\u5024\u304c 2 \u4ee5\u4e0b\u306e\u5834\u5408\u3001\u89e3\u306f\u7121\u9650\u306b\u3042\u308a\u307e\u3059\u3002 n<\/i> = 1 \u306e<\/span>\u5834\u5408\u306f\u660e\u3089\u304b\u3067\u3059\u3002 n<\/i> = 2<\/span>\u306e\u5834\u5408\u3001\u7279\u306b\u53e4\u5178\u7684\u306a\u89e3 3 2<\/sup> + 4 2<\/sup> = 5 2<\/sup>\u304c\u8a8d\u3081\u3089\u308c\u307e\u3059\u3002\u4e00\u822c\u306b\u3001 n<\/i> = 2<\/span>\u306e\u3059\u3079\u3066\u306e\u89e3\u306f\u3001x=2kml\u3001y=k(m 2<\/sup> -l 2<\/sup> )\u3001z=k(m 2<\/sup> +l 2<\/sup> ) \u3067\u4e0e\u3048\u3089\u308c\u307e\u3059<\/a><\/span>\u3002\u3053\u3053\u3067\u3001\u6570\u5024 k\u3001l\u3001m \u306f\u6761\u4ef6\u3092\u6e80\u305f\u3057\u307e\u3059\u3002 : \u6574\u6570 k\u3001m>l\u3001m \u3068 l \u306e\u7570\u306a\u308b\u30d1\u30ea\u30c6\u30a3\u3002\u3053\u308c\u3089\u306e\u6574\u6570\u306f\u3001\u30d4\u30bf\u30b4\u30e9\u30b9 \u30c8\u30ea\u30d7\u30eb\u3068\u547c\u3070\u308c\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002\u305f\u3060\u3057\u3001 n \u304c<\/i><\/span>2 \u3088\u308a\u5927\u304d\u304f\u306a\u308b\u3068\u3001\u3053\u308c\u306f\u4e0d\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002<\/p>