{"id":74293,"date":"2023-11-16T02:42:16","date_gmt":"2023-11-16T02:42:16","guid":{"rendered":"https:\/\/science-hub.click\/%E4%BA%8C%E6%AC%A1%E3%82%B9%E3%82%AF%E3%83%AA%E3%83%BC%E3%83%B3-%E5%AE%9A%E7%BE%A9\/"},"modified":"2023-11-16T02:42:16","modified_gmt":"2023-11-16T02:42:16","slug":"%E4%BA%8C%E6%AC%A1%E3%82%B9%E3%82%AF%E3%83%AA%E3%83%BC%E3%83%B3-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=74293","title":{"rendered":"\u4e8c\u6b21\u30b9\u30af\u30ea\u30fc\u30f3 &#8211; \u5b9a\u7fa9"},"content":{"rendered":"<div><div><h2>\u5c0e\u5165<\/h2><p><b>\u4e8c\u6b21\u3075\u308b\u3044<\/b>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u30e2\u30b8\u30e5\u30e9\u30fc\u6f14\u7b97\u306b\u57fa\u3065\u304f\u56e0\u6570\u5206\u89e3\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u3002\u5b9f\u969b\u306b\u306f\u3001\u3053\u308c\u306f\u6570\u5024\u30d5\u30a3\u30fc\u30eb\u30c9\u3067\u306e\u4e00\u822c\u5316\u3055\u308c\u305f\u30b9\u30af\u30ea\u30fc\u30cb\u30f3\u30b0\u306e\u5f8c\u3067\u6700\u3082\u9ad8\u901f\u3067\u3059\u304c\u3001\u306f\u308b\u304b\u306b\u8907\u96d1\u3067\u3001\u5c11\u306a\u304f\u3068\u3082 10 \u9032\u6570 100 \u6841\u306e<span><a href=\"https:\/\/science-hub.click\/?p=71097\">\u6574\u6570<\/a><\/span>\u3092\u56e0\u6570\u5206\u89e3\u3059\u308b\u5834\u5408\u306b\u306e\u307f\u52b9\u7387\u7684\u3067\u3059\u3002<span><a href=\"https:\/\/science-hub.click\/?p=74293\">\u4e8c\u6b21\u3075\u308b\u3044\u306f<\/a><\/span>\u3001\u7279\u6b8a\u5316\u3055\u308c\u3066\u3044\u306a\u3044\u56e0\u6570\u5206\u89e3\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u305d\u306e\u5b9f\u884c<span><a href=\"https:\/\/science-hub.click\/?p=82055\">\u6642\u9593\u306f<\/a><\/span>\u56e0\u6570\u5206\u89e3\u3055\u308c\u308b\u6574\u6570\u306e\u30b5\u30a4\u30ba\u306e\u307f\u306b\u4f9d\u5b58\u3057\u3001\u6574\u6570\u306e\u7279\u5b9a\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u306b\u306f\u4f9d\u5b58\u3057\u307e\u305b\u3093\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u4e8c\u6b21\u30b9\u30af\u30ea\u30fc\u30f3 - \u5b9a\u7fa9\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/1K4EDL9Swzk\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2>\u57fa\u672c\u76ee\u6a19<\/h2><p>1981 \u5e74\u306b Carl Pomerance \u306b\u3088\u3063\u3066<span><a href=\"https:\/\/science-hub.click\/?p=43578\">\u958b\u767a\u3055\u308c\u305f<\/a><\/span>\u3053\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001Dixon \u306e\u56e0\u6570\u5206\u89e3\u6cd5\u3092<span>\u6539\u826f\u3057\u305f\u3082\u306e<\/span>\u3067\u3001\u305d\u308c\u81ea\u4f53\u306f\u30d5\u30a7\u30eb\u30de\u30fc\u306e\u56e0\u6570\u5206\u89e3\u6cd5\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002 <i>n<\/i> (\u56e0\u6570\u5206\u89e3\u3055\u308c\u308b\u6574\u6570) \u3092\u6cd5\u3068\u3059\u308b\u4e8c\u4e57\u306e<span><a href=\"https:\/\/science-hub.click\/?p=28224\">\u5408\u540c<\/a><\/span>\u3092\u78ba\u7acb\u3057\u3088\u3046\u3068\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u591a\u304f\u306e\u5834\u5408\u3001\u6b21\u306e\u56e0\u6570\u5206\u89e3\u306b\u3064\u306a\u304c\u308a\u307e\u3059\u3002 <i>n<\/i> \u3002<\/p><p>\u3053\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f 2 \u3064\u306e\u30d5\u30a7\u30fc\u30ba\u3067\u52d5\u4f5c\u3057\u307e\u3059\u3002<\/p><ul><li><i>\u30c7\u30fc\u30bf\u53ce\u96c6<\/i><span><a href=\"https:\/\/science-hub.click\/?p=15396\">\u30d5\u30a7\u30fc\u30ba<\/a><\/span>\u3067\u306f\u3001\u6b63\u65b9\u5f62\u306e\u5408\u540c\u306b\u3064\u306a\u304c\u308b\u53ef\u80fd\u6027\u306e\u3042\u308b\u60c5\u5831\u3092\u53ce\u96c6\u3057\u307e\u3059\u3002<\/li><li><i>\u30c7\u30fc\u30bf\u6d3b\u7528<\/i>\u30d5\u30a7\u30fc\u30ba\u3067\u306f\u3001\u53ce\u96c6\u3057\u305f\u3059\u3079\u3066\u306e\u30c7\u30fc\u30bf\u3092\u884c\u5217\u306b\u914d\u7f6e\u3057\u3001\u305d\u308c\u3092\u89e3\u3044\u3066\u6b63\u65b9\u5f62\u306e\u5408\u540c\u3092\u6c42\u3081\u307e\u3059\u3002<\/li><\/ul><p>\u53ce\u96c6\u30d5\u30a7\u30fc\u30ba\u306f\u7c21\u5358\u304b\u3064\u52b9\u7387\u7684\u306b\u4e26\u5217\u5316\u3067\u304d\u307e\u3059\u304c\u3001\u6d3b\u7528\u30d5\u30a7\u30fc\u30ba\u306f\u4e26\u5217\u5316\u3067\u304d\u307e\u305b\u3093\u3002\u305f\u3060\u3057\u3001\u30b5\u30d6\u30b7\u30b9\u30c6\u30e0\u306e\u6570\u304c\u5c11\u306a\u304f\u3001\u305d\u308c\u305e\u308c\u306e\u30b5\u30d6\u30b7\u30b9\u30c6\u30e0\u306b\u884c\u5217\u5168\u4f53\u3092\u683c\u7d0d\u3059\u308b\u306e\u306b\u5341\u5206\u306a<span><a href=\"https:\/\/science-hub.click\/?p=40158\">\u30e1\u30e2\u30ea<\/a><\/span>\u304c\u3042\u308b\u5834\u5408\u3092\u9664\u304d\u307e\u3059 (\u3053\u306e\u5834\u5408\u3001 <span title=\"Wiedemann \u30d6\u30ed\u30c3\u30af \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 (\u30da\u30fc\u30b8\u304c\u5b58\u5728\u3057\u307e\u305b\u3093)\">Wiedemann \u30d6\u30ed\u30c3\u30af \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092<\/span>\u4f7f\u7528\u3067\u304d\u307e\u3059<span title=\"\u5225\u306e\u8a00\u8a9e\u306e\u8a18\u4e8b\u300cWiedemann \u30d6\u30ed\u30c3\u30af \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u300d\u306b\u76f8\u5f53\">)\u3002<\/span><\/p><p>\u5e73\u65b9\u306e\u5408\u540c\u3092\u898b\u3064\u3051\u308b\u7d20\u6734\u306a\u30a2\u30d7\u30ed\u30fc\u30c1\u306f\u3001\u6570\u5024\u3092<span><a href=\"https:\/\/science-hub.click\/?p=103037\">\u30e9\u30f3\u30c0\u30e0<\/a><\/span>\u306b\u9078\u629e\u3057\u3001\u305d\u308c\u3092<span><a href=\"https:\/\/science-hub.click\/?p=94249\">\u5e73\u65b9\u3057<\/a><\/span>\u3001 <i>n<\/i>\u3092\u6cd5\u3068\u3057\u305f\u6700\u5c0f\u306e\u5270\u4f59 (\u6b63\u307e\u305f\u306f\u30bc\u30ed) \u304c<span><a href=\"https:\/\/science-hub.click\/?p=70063\">\u5b8c\u5168\u306a\u5e73\u65b9<\/a><\/span>(\u3064\u307e\u308a\u3001\u5168\u4f53\u306e 2 \u4e57) \u3067\u3042\u308b\u3053\u3068\u3092\u671f\u5f85\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u30e2\u30b8\u30e5\u30ed 5959 \u3067\u306f\u3001\u6574\u6570 80 <sup>2<\/sup>\u306f 441=21 <sup>2<\/sup>\u306b\u4e00\u81f4\u3057\u307e\u3059\u3002 <i>n<\/i>\u304c\u5927\u304d\u3044\u5834\u5408\u3001\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u3067\u5e73\u65b9\u306e\u5408\u540c\u304c\u898b\u3064\u304b\u308b\u3053\u3068\u306f\u3081\u3063\u305f\u306b\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u3053\u308c\u304c\u767a\u751f\u3057\u305f\u5834\u5408\u3001\u3053\u306e\u5408\u540c\u306f\u307b\u3068\u3093\u3069\u306e\u5834\u5408\u81ea\u660e\u3067\u306f\u306a\u3044\u305f\u3081\u3001 <i>n \u3092<\/i>\u56e0\u6570\u5206\u89e3\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p><p>\u6574\u6570<i>n \u3092<\/i>\u56e0\u6570\u5206\u89e3\u3059\u308b\u4e8c\u6b21\u3075\u308b\u3044\u306e\u5b9f\u884c\u6642\u9593\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {O\\left(e^\\sqrt{\\log n \\log\\log n}\\right)=L_n\\left[1\/2,1\\right]} $$<\/div><\/dd><\/dl><p> Landau \u306e O \u8a18\u6cd5\u3068<span title=\"L\u8868\u8a18\uff08\u30da\u30fc\u30b8\u7121\u3057\uff09\">L \u8a18\u6cd5<\/span>\u3092\u4f7f\u7528\u3057\u307e\u3059<span title=\"\u4ed6\u8a00\u8a9e\u306e\u51a0\u8a5e\u300cL\u8868\u8a18\u300d\u306b\u76f8\u5f53\">\u3002<\/span><\/p><h2>\u8907\u6570\u306e\u591a\u9805\u5f0f<\/h2><p>\u5b9f\u969b\u306b\u306f\u3001\u5358\u4e00\u306e<span><a href=\"https:\/\/science-hub.click\/?p=35323\">\u591a\u9805\u5f0f<\/a><\/span><i>y<\/i> ( <i>x<\/i> ) = <i>x2<\/i> <sup>\u2212<\/sup> <i>n<\/i>\u3067\u306f\u3001\u56e0\u5b50\u306b\u57fa\u3065\u304f\u5341\u5206\u306a\u6b63\u898f ( <i>x<\/i> , <i>y<\/i> ) \u304c\u5f97\u3089\u308c\u307e\u305b\u3093\u3002\u6b21\u306b\u3001\u591a\u9805\u5f0f\u306e\u65cf\u5168\u4f53\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002 <i>n<\/i>\u3092\u6cd5\u3068\u3059\u308b\u5e73\u65b9\u306b\u306a\u308b\u306b\u306f\u3001\u5143\u306e\u591a\u9805\u5f0f\u3068\u540c\u69d8\u306e\u5f62\u5f0f\u3067\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {y(x)=(Ax+B)^2-n \\qquad A,B\\in\\mathbb{Z}~.} $$<\/div><\/dd><\/dl><p>\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306f\u3001\u591a\u91cd\u591a\u9805\u5f0f\u4e8c\u6b21\u30b9\u30af\u30ea\u30fc\u30cb\u30f3\u30b0\u3068\u547c\u3070\u308c\u3001\u4e26\u5217\u5316\u306b\u6700\u9069\u3067\u3059\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u4e8c\u6b21\u30b9\u30af\u30ea\u30fc\u30f3 - \u5b9a\u7fa9\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/TVVx7ViAru0\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2>\u5408\u540c\u5f0f\u306e\u63a2\u7d22\u306e\u6700\u9069\u5316<\/h2><p>\u4e8c\u6b21\u3075\u308b\u3044\u306f\u3001 <i>x<\/i> <sup>2<\/sup> \u2261 <i>y<\/i> <sup>2<\/sup> (mod <i>n<\/i> ) \u3088\u308a\u3082\u306f\u308b\u304b\u306b\u5f31\u3044\u6761\u4ef6\u3092\u6e80\u305f\u3059\u3001\u6574\u6570<i>x<\/i>\u3068<i>y(x)<\/i> ( <i>y(x)<\/i>\u306f<i>x<\/i>\u306e\u95a2\u6570) \u306e\u30da\u30a2\u3092\u898b\u3064\u3051\u3088\u3046\u3068\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001 <i>factor Base<\/i>\u3068\u547c\u3070\u308c\u308b<span><a href=\"https:\/\/science-hub.click\/?p=104095\">\u7d20\u6570\u306e\u30bb\u30c3\u30c8<\/a><\/span>\u3092\u9078\u629e\u3057\u3001 <i>n<\/i>\u3092\u6cd5\u3068\u3059\u308b<i>x<\/i> <sup>2<\/sup>\u306e\u300c\u6700\u5c0f\u7d76\u5bfe\u5270\u4f59\u300d <i>y(x)<\/i>\u304c\u3053\u306e\u300cbase\u300d\u3067<span>\u5b8c\u5168\u306b<\/span>\u56e0\u6570\u5206\u89e3\u3055\u308c\u308b<i>x<\/i>\u3092\u63a2\u3057\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u6574\u6570\u306e\u30da\u30a2\u306f\u3001\u3053\u306e\u57fa\u6570\u306b\u5bfe\u3057\u3066<i>\u898f\u5247\u7684\u3067\u3042\u308b<\/i>\u3068\u8a00\u308f\u308c\u3001\u57fa\u6570\u3067\u306e<i>y(x)<\/i>\u306e\u56e0\u6570\u5206\u89e3\u3068<i>x<\/i>\u306e\u5024\u306e\u7d44\u307f\u5408\u308f\u305b\u306f\u3001\u3044\u308f\u3086\u308b<i>\u95a2\u4fc2<\/i>\u3092\u69cb\u6210\u3057\u307e\u3059\u3002\u4e8c\u6b21\u3075\u308b\u3044\u306f\u3001 <i>x \u3092<\/i><i>n<\/i>\u306e<span><a href=\"https:\/\/science-hub.click\/?p=93175\">\u5e73\u65b9\u6839<\/a><\/span>\u306b\u8fd1\u3065\u3051\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u95a2\u4fc2\u3092\u898b\u3064\u3051\u308b\u30d7\u30ed\u30bb\u30b9\u3092\u9ad8\u901f\u5316\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001 <i>y(x) \u306f<\/i>\u5c0f\u3055\u304f\u306a\u308a\u3001\u3057\u305f\u304c\u3063\u3066\u300c\u6b63\u898f\u300d\u3067\u3042\u308b\u53ef\u80fd\u6027\u304c\u9ad8\u304f\u306a\u308a\u307e\u3059\u3002 <i>x<\/i> =[\u221a <i>n<\/i> ]+ <i>z<\/i> ( <i>z<\/i>\u6574\u6570\u304c\u300c\u5c0f\u3055\u3044\u300d) \u306e\u5834\u5408\u3001 <\/p><center><div class=\"math-formual notranslate\">$$ {y(x)=x^2-n=\\left(\\left\\lfloor\\sqrt{n}\\right\\rfloor+z\\right)^2-n\\approx 2z\\left\\lfloor\\sqrt{n}\\right\\rfloor\\ .} $$<\/div><\/center><p>\u305f\u3060\u3057\u3001\u3053\u308c\u306f<i>y \u304c<\/i><i>z<\/i>\u306b\u5fdc\u3058\u3066\u7dda\u5f62\u306b\u5897\u52a0\u3059\u308b\u3053\u3068\u3082\u610f\u5473\u3057\u307e\u3059\u3002<\/p><p>\u6574\u5408\u6027\u306e\u53ef\u80fd\u6027\u3092\u9ad8\u3081\u308b\u3082\u3046 1 \u3064\u306e\u65b9\u6cd5\u306f\u3001\u5358\u7d14\u306b\u30c7\u30fc\u30bf\u30d9\u30fc\u30b9\u306e\u30b5\u30a4\u30ba\u3092\u5897\u3084\u3059\u3053\u3068\u3067\u3059\u304c\u3001\u3053\u308c\u306b\u306f\u3088\u308a\u591a\u304f\u306e\u95a2\u4fc2\u3092\u53ce\u96c6\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u5b9f\u969b\u3001\u95a2\u4fc2\u304c\u7dda\u5f62\u4f9d\u5b58\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3059\u308b\u306b\u306f\u3001\u57fa\u5e95\u306e\u7d20\u56e0\u6570\u306e\u6570\u3088\u308a\u5c11\u306a\u304f\u3068\u3082 1 \u3064\u591a\u304f\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u4e8c\u6b21\u30b9\u30af\u30ea\u30fc\u30f3 - \u5b9a\u7fa9\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/cFM2iXm6aUM\/0.jpg\" style=\"width:100%;\"\/><\/figure><h3><span>\u90e8\u5206\u7684\u306a\u95a2\u4fc2\u3068\u30b5\u30a4\u30af\u30eb<\/span><\/h3><p>\u95a2\u4fc2\u306b\u304a\u3044\u3066<i>y(x) \u304c<\/i>\u898f\u5247\u7684\u3067\u306a\u3044\u5834\u5408\u3067\u3082\u3001\u305d\u306e\u3088\u3046\u306a 2 \u3064<i>\u306e\u90e8\u5206\u95a2\u4fc2<\/i>\u3092\u30de\u30fc\u30b8\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u300c\u5b8c\u5168\u306a\u300d\u95a2\u4fc2\u304c\u5f62\u6210\u3055\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u304c\u8d77\u3053\u308b\u305f\u3081\u306b\u306f\u3001\u57fa\u5e95\u306e\u5916\u5074\u3067 2 \u3064\u306e\u7d20\u56e0\u6570<i>\u304c<\/i>\u540c\u3058\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u57fa\u6570\u304c {2, 3, 5, 7} \u3067<i>n<\/i> = 91 \u306e\u5834\u5408\u30012 \u3064\u306e\u90e8\u5206\u95a2\u4fc2\u306e\u7a4d\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {21^2\\equiv7^1\\cdot11\\pmod{91}} $$<\/div>\u305d\u3057\u3066<\/dd><dd><div class=\"math-formual notranslate\">$$ {29^2\\equiv2^1\\cdot11\\pmod{91}} $$<\/div><\/dd><\/dl><p>\u79c1\u305f\u3061\u306f\u5f97\u308b<\/p><dl><dd><div class=\"math-formual notranslate\">$$ {(21\\cdot 29)^2\\equiv2^1\\cdot7^1\\cdot11^2\\pmod{91}~.} $$<\/div><\/dd><\/dl><p> 2 \u3064\u306e\u8fba\u306b 11 <sup>-1<\/sup>\u306e 91 \u3092\u6cd5\u3068\u3059\u308b 2 \u4e57\u3001\u3064\u307e\u308a 58 (\u305f\u3068\u3048\u3070\u3001\u62e1\u5f35<span><a href=\"https:\/\/science-hub.click\/?p=40098\">Euclid<\/a><\/span>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u7528\u3057\u3066\u53d6\u5f97\u3055\u308c\u305f\u5024) \u3092\u4e57\u7b97\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u5b8c\u5168\u306a\u95a2\u4fc2\u3092\u63a8\u5b9a\u3057\u307e\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {(58\\cdot 21\\cdot 29)^2\\equiv 2^1\\cdot7^1\\pmod{91}~,} $$<\/div>\u3069\u3061\u3089\u304b<\/dd><dd><div class=\"math-formual notranslate\">$$ {14^2\\equiv 2^1\\cdot7^1\\pmod{91}~.} $$<\/div><\/dd><\/dl><p>\u3053\u306e\u3088\u3046\u306a\u5b8c\u5168\u306a\u95a2\u4fc2\uff08\u90e8\u5206\u95a2\u4fc2\u306e<span>\u7d44\u307f\u5408\u308f\u305b<\/span>\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u308b\uff09\u3092<i>\u30b5\u30a4\u30af\u30eb<\/i>\u3068\u547c\u3073\u307e\u3059\u3002\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u30012 \u3064\u306e\u90e8\u5206\u95a2\u4fc2\u304b\u3089\u306e\u30b5\u30a4\u30af\u30eb\u306e\u5f62\u6210\u304c\u6b63\u65b9\u5f62\u306e\u5408\u540c\u306b\u76f4\u63a5\u3064\u306a\u304c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u305d\u308c\u306f\u307e\u308c\u3067\u3059\u3002<\/p><h3><span>\u30b9\u30af\u30ea\u30fc\u30cb\u30f3\u30b0\u306b\u3088\u308b\u898f\u5247\u6027\u306e\u78ba\u8a8d<\/span><\/h3><p><i>y<\/i>\u306e\u898f\u5247\u6027\u3092\u78ba\u8a8d\u3059\u308b\u306b\u306f\u3044\u304f\u3064\u304b\u306e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u6700\u3082\u660e\u767d\u306a\u306e\u306f\u5206\u5272\u30c6\u30b9\u30c8\u65b9\u6cd5\u3067\u3059\u304c\u3001\u3053\u308c\u306b\u3088\u308a\u30c7\u30fc\u30bf\u53ce\u96c6\u30d5\u30a7\u30fc\u30ba\u306e\u6240\u8981\u6642\u9593\u304c\u5897\u52a0\u3057\u307e\u3059\u3002\u6955\u5186\u66f2\u7dda\u6cd5\u3082\u6642\u3005\u4f7f\u7528\u3055\u308c\u308b\u5225\u306e\u65b9\u6cd5\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u6700\u3082\u4e00\u822c\u7684\u306a\u65b9\u6cd5\u306f<i>\u3001\u30b9\u30af\u30ea\u30fc\u30cb\u30f3\u30b0<\/i>\u306b\u3088\u3063\u3066\u7d9a\u884c\u3059\u308b\u3053\u3068\u3067\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {y(x)=x^2-n\\,\\!} $$<\/div><\/dd><dd><div class=\"math-formual notranslate\">$$ {y(x+kp)=(x+kp)^2-n\\,\\!} $$<\/div><\/dd><dd><div class=\"math-formual notranslate\">$$ {y(x+kp)=x^2+2xkp+(kp)^2-n\\,\\!} $$<\/div><\/dd><dd><div class=\"math-formual notranslate\">$$ {y(x+kp)=y(x)+2xkp+(kp)^2\\equiv y(x)\\pmod{p}} $$<\/div><\/dd><\/dl><p>\u7b54\u3048\u3066\u304f\u3060\u3055\u3044\u3002y <i>(x)<\/i> \u2261 0 (mod <i>p<\/i> ) \u3068\u306a\u308b\u3088\u3046\u306a<i>x \u304c<\/i>\u308f\u304b\u3063\u3066\u3044\u308b\u5834\u5408\u3001 <i>p<\/i>\u3067\u5272\u308a\u5207\u308c\u308b<i>y<\/i>\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u5168\u4f53\u3092\u63a8\u5b9a\u3057\u307e\u3059\u3002 <i>p<\/i>\u306e\u4ed6\u306e\u5024\u306b\u5bfe\u3057\u3066\u3053\u306e\u30d7\u30ed\u30bb\u30b9\u3092\u7e70\u308a\u8fd4\u3059\u3053\u3068\u3067\u3001\u6bce\u56de\u898f\u5247\u6027\u3092\u30c6\u30b9\u30c8\u3059\u308b\u5fc5\u8981\u304c\u306a\u304f (\u3053\u306e<span><a href=\"https:\/\/science-hub.click\/?p=107477\">\u4f53\u7cfb\u7684\u306a<\/a><\/span>\u30c6\u30b9\u30c8\u306b\u306f\u6642\u9593\u304c\u304b\u304b\u308a\u3059\u304e\u307e\u3059)\u3001\u30b9\u30af\u30ea\u30fc\u30cb\u30f3\u30b0 \u30d7\u30ed\u30bb\u30b9 (\u30a8\u30e9\u30c8\u30b9\u30c6\u30cd\u30b9\u306e\u3075\u308b\u3044\u306b\u4f3c\u3066\u3044\u307e\u3059) \u3092\u901a\u3058\u3066\u898f\u5247\u7684\u306a\u5024\u304c\u898b\u3064\u304b\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u56e0\u6570\u5206\u89e3\u30ec\u30b3\u30fc\u30c9\u306e\u3088\u3046\u306a\u5927\u304d\u306a\u6570\u306e\u5834\u5408)\u3002\u3053\u306e\u30d7\u30ed\u30bb\u30b9\u4e2d\u306b\u3001\u53ce\u96c6\u3055\u308c\u305f\u901a\u5e38\u306e<i>y<\/i>\u306e\u56e0\u6570\u5206\u89e3\u306e\u8a73\u7d30\u306a\u60c5\u5831\u304c\u5931\u308f\u308c\u307e\u3059\u304c\u3001\u300c\u5c0f\u3055\u306a\u300d\u56e0\u6570 (\u57fa\u6570\u306e\u56e0\u6570) \u3057\u304b\u306a\u3044\u305f\u3081\u3001\u3059\u3050\u306b\u518d\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p><\/div><h2 class=\"ref_link\">\u53c2\u8003\u8cc7\u6599<\/h2><ol><li><a class=\"notranslate\" href=\"https:\/\/de.wikipedia.org\/wiki\/Quadratisches_Sieb\">Quadratisches Sieb \u2013 allemand<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/en.wikipedia.org\/wiki\/Quadratic_sieve\">Quadratic sieve \u2013 anglais<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/es.wikipedia.org\/wiki\/Criba_cuadr%C3%A1tica\">Criba cuadr\u00e1tica \u2013 espagnol<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/fi.wikipedia.org\/wiki\/Neli%C3%B6seula\">Neli\u00f6seula \u2013 finnois<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/he.wikipedia.org\/wiki\/%D7%A0%D7%A4%D7%94_%D7%A8%D7%99%D7%91%D7%95%D7%A2%D7%99%D7%AA\">\u05e0\u05e4\u05d4 \u05e8\u05d9\u05d1\u05d5\u05e2\u05d9\u05ea \u2013 h\u00e9breu<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/it.wikipedia.org\/wiki\/Crivello_quadratico\">Crivello quadratico \u2013 italien<\/a><\/li><\/ol><\/div>\n<div class=\"feature-video\">\n <h2>\n  \u4e8c\u6b21\u30b9\u30af\u30ea\u30fc\u30f3 &#8211; \u5b9a\u7fa9\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n <div class=\"video-item\">\n  \n  <figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\">\n   <div class=\"wp-block-embed__wrapper\">\n    <iframe loading=\"lazy\" title=\"\u771f\u76f8\u3092\u77e5\u3089\u306a\u3044\u65b9\u304c\u3057\u3042\u308f\u305b\u304b\u3082\u3057\u308c\u307e\u305b\u3093(\u7dcf\u96c6\u7de8)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/N1l8_szM6co?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n   <\/div>\n  <\/figure>\n  \n <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5c0e\u5165 \u4e8c\u6b21\u3075\u308b\u3044\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u30e2\u30b8\u30e5\u30e9\u30fc\u6f14\u7b97\u306b\u57fa\u3065\u304f\u56e0\u6570\u5206\u89e3\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u3002\u5b9f\u969b\u306b\u306f\u3001\u3053\u308c\u306f\u6570\u5024\u30d5\u30a3\u30fc\u30eb\u30c9\u3067\u306e\u4e00\u822c\u5316\u3055\u308c\u305f\u30b9\u30af\u30ea\u30fc\u30cb\u30f3\u30b0\u306e\u5f8c\u3067\u6700\u3082\u9ad8\u901f\u3067\u3059\u304c\u3001\u306f\u308b\u304b\u306b\u8907\u96d1\u3067\u3001\u5c11\u306a\u304f\u3068\u3082 10 \u9032\u6570 100 \u6841\u306e\u6574\u6570\u3092 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":74294,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/img.youtube.com\/vi\/WSAEruWtkcg\/0.jpg","fifu_image_alt":"\u4e8c\u6b21\u30b9\u30af\u30ea\u30fc\u30f3 - \u5b9a\u7fa9","footnotes":""},"categories":[5],"tags":[68133,11,13,14,10,5238,12,8,41499,16,15,9],"class_list":["post-74293","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dictionary","tag-partage-de-code","tag-techniques","tag-technologie","tag-news","tag-actualite","tag-quadratique","tag-dossier","tag-definition","tag-crible","tag-sciences","tag-article","tag-explications"],"_links":{"self":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/74293"}],"collection":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=74293"}],"version-history":[{"count":0,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/74293\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/media\/74294"}],"wp:attachment":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=74293"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=74293"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=74293"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}