{"id":100749,"date":"2024-06-13T21:41:07","date_gmt":"2024-06-13T21:41:07","guid":{"rendered":"https:\/\/science-hub.click\/%E3%83%87%E3%82%A3%E3%82%AA%E3%83%95%E3%82%A1%E3%83%B3%E3%83%88%E3%82%B9%E6%96%B9%E7%A8%8B%E5%BC%8Fax%2Bby%3Dc-%E5%AE%9A%E7%BE%A9\/"},"modified":"2024-06-13T21:41:07","modified_gmt":"2024-06-13T21:41:07","slug":"%E3%83%87%E3%82%A3%E3%82%AA%E3%83%95%E3%82%A1%E3%83%B3%E3%83%88%E3%82%B9%E6%96%B9%E7%A8%8B%E5%BC%8Fax%2Bby%3Dc-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=100749","title":{"rendered":"\u30c7\u30a3\u30aa\u30d5\u30a1\u30f3\u30c8\u30b9\u65b9\u7a0b\u5f0f ax+by = c &#8211; \u5b9a\u7fa9"},"content":{"rendered":"<div><div><h2>\u5c0e\u5165<\/h2><p><b>\u65b9\u7a0b\u5f0f ax + by = c<\/b> (\u4fc2\u6570 a\u3001b\u3001c \u306f 3 \u3064\u306e\u76f8\u5bfe\u6574\u6570\u3001\u672a\u77e5\u6570 x \u3068 y \u306f\u76f8\u5bfe\u6574\u6570) \u306f\u3001\u89e3\u304f\u306e\u304c\u6700\u3082\u7c21\u5358\u306a\u30c7\u30a3\u30aa\u30d5\u30a1\u30f3\u30c8\u30b9\u65b9\u7a0b\u5f0f\u306e 1 \u3064\u3067\u3059\u3002\u305d\u306e\u89e3\u6c7a\u7b56\u306f\u3001 <span><a href=\"https:\/\/science-hub.click\/?p=40098\">Euclid<\/a><\/span>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3001 <span><a href=\"https:\/\/science-hub.click\/?p=20306\">Bachet-B\u00e9zout \u306e\u5b9a\u7406\u3001<\/a><\/span>\u304a\u3088\u3073<span><a href=\"https:\/\/science-hub.click\/?p=96577\">\u30ac\u30a6\u30b9\u306e\u5b9a\u7406<\/a><\/span>\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002 c \u304c a \u3068 b \u306e GCD \u306b\u7b49\u3057\u3044\u5834\u5408\u3001\u305d\u308c\u306f<b>\u30d9\u30ba\u30fc\u6052\u7b49\u5f0f<\/b>\u3068\u547c\u3070\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002<\/p><p>\u76f8\u5bfe\u6574\u6570\u306e<span><a href=\"https:\/\/science-hub.click\/?p=57227\">\u30bb\u30c3\u30c8<\/a><\/span>\u3067\u306f\u3001\u305d\u306e\u3088\u3046\u306a\u65b9\u7a0b\u5f0f\u306b\u306f\u89e3\u304c\u306a\u3044\u304b\u3001\u7121\u9650\u306b\u89e3\u304c\u5b58\u5728\u3057\u307e\u3059\u3002\u4fc2\u6570\u3068\u672a\u77e5\u6570\u304c\u81ea\u7136\u6570\u306e\u5834\u5408\u3001\u65b9\u7a0b\u5f0f\u306e\u89e3\u306e<span><a href=\"https:\/\/science-hub.click\/?p=71097\">\u6570\u306f<\/a><\/span>\u6709\u9650\u306b\u306a\u308a\u307e\u3059\u3002\u30d1\u30aa\u30ea\u306e<span>\u5b9a\u7406\u306b\u3088\u308a<\/span>\u6570\u5024\u306f 1 \u4ee5\u5185\u306b\u306a\u308a\u307e\u3059\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u30c7\u30a3\u30aa\u30d5\u30a1\u30f3\u30c8\u30b9\u65b9\u7a0b\u5f0f ax+by = c - \u5b9a\u7fa9\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/E8H2AqPYLeg\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2>\u76f8\u5bfe\u6574\u6570\u306e\u30bb\u30c3\u30c8\u5185\u306e\u89e3\u3092\u898b\u3064\u3051\u308b<\/h2><h3><span><span><a href=\"https:\/\/science-hub.click\/?p=66517\">\u65b9\u7a0b\u5f0f<\/a><\/span>ax + by = 1 \u3053\u3053\u3067\u3001a \u3068 b \u306f\u4e92\u3044\u306b\u7d20\u3067\u3059<\/span><\/h3><p>\u30d0\u30b7\u30a7\u30fb\u30d9\u30ba\u30fc\u306e\u5b9a\u7406\u306f\u3001\u3053\u306e\u65b9\u7a0b\u5f0f\u306f\u5e38\u306b\u5c11\u306a\u304f\u3068\u3082 1 \u3064\u306e\u89e3\u3092\u8a31\u5bb9\u3059\u308b\u3068\u8ff0\u3079\u3066\u3044\u307e\u3059\u3002<\/p><p>\u89e3\u6c7a\u306e\u6700\u521d\u306e\u30b9\u30c6\u30c3\u30d7\u306f\u3001\u7279\u5b9a\u306e\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002\u3064\u307e\u308a\u3001ax <sub>0<\/sub> + by <sub>0<\/sub> = 1 \u3092\u691c\u8a3c\u3059\u308b\u76f8\u5bfe\u6574\u6570\u306e\u30da\u30a2 (x <sub>0<\/sub> , y <sub>0<\/sub> ) \u3092\u898b\u3064\u3051\u307e\u3059\u3002<\/p><ul><li>\u62e1\u5f35 Euclid \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u305d\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u304d\u307e\u3059\u3002<\/li><li>\u3082\u3046 1 \u3064\u306e\u65b9\u6cd5\u306f\u3001a\/b \u306e<span><a href=\"https:\/\/science-hub.click\/?p=50712\">\u9023\u5206\u6570<\/a><\/span>\u5c55\u958b\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u6700\u5f8c\u304b\u3089 2 \u756a\u76ee\u306e\u63db\u7b97\u306b\u3088\u308a\u554f\u984c\u306e\u89e3\u6c7a\u7b56\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\frac{h_{n-1}}{k_{n-1}}} $$<\/div>\u6700\u5f8c\u304b\u3089 2 \u756a\u76ee\u306f\u6b21\u306e\u3088\u3046\u306b\u6e1b\u7b97\u3055\u308c\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\frac ab} $$<\/div>\u3059\u308b\u3068<span><i>k<\/i> <sub><i>n<\/i> \u2212 1<\/sub> <i>a<\/i> \u2212 <i>h<\/i> <sub><i>n<\/i> \u2212 1<\/sub> <i>b<\/i> = (\u2212 1) <sup><i>n<\/i> + 1 \u3068\u306a\u308a\u307e\u3059<\/sup><\/span>\u3002<\/li><li>\u3057\u304b\u3057\u3001b \u304c\u5927\u304d\u3059\u304e\u306a\u3044\u5834\u5408\u306f\u3001b \u3092\u6cd5\u3068\u3057\u3066\u8a08\u7b97\u3057\u30011 \u3068 |b| \u306e\u9593\u306e\u6574\u6570 x <sub>0<\/sub>\u3092\u63a2\u3059\u5358\u7d14\u306a<span><a href=\"https:\/\/science-hub.click\/?p=28224\">\u30b9\u30ad\u30e3\u30f3<\/a><\/span>\u306b\u3088\u3063\u3066\u89e3\u3092\u63a2\u3059\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002 &#8211; 1\u3001\u30c1\u30a7\u30c3\u30af\u4e2d<div class=\"math-formual notranslate\">$$ {ax \\equiv 1 \\pmod b} $$<\/div> \u3001\u6574\u6570 y <sub>0<\/sub>\u306f\u6b21\u3068\u7b49\u3057\u3044\u3082\u306e\u3068\u3057\u3066\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\frac{1-ax_0}{b}} $$<\/div> \u3002<\/li><\/ul><div><p><strong>\u89e3\u306e\u30bb\u30c3\u30c8<\/strong><span>\u2014<\/span>\u7279\u5b9a\u306e\u89e3 (x <sub>0<\/sub> , y <sub>0<\/sub> ) \u304c\u65e2\u77e5\u3067\u3042\u308b\u5834\u5408\u3001\u89e3\u306e\u30bb\u30c3\u30c8\u306f\u30da\u30a2 (x <sub>0<\/sub> +bk, y <sub>0<\/sub> &#8211; ak) \u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002\u3053\u3053\u3067\u3001k \u306f<span><a href=\"https:\/\/science-hub.click\/?p=7734\">\u4efb\u610f\u306e\u76f8\u5bfe\u6574\u6570<\/a><\/span>\u3067\u3059\u3002<\/p><\/div><p>\u5b9f\u969b\u3001\u3053\u306e\u3088\u3046\u306a\u30ab\u30c3\u30d7\u30eb\u304c\u554f\u984c\u306e\u89e3\u6c7a\u7b56\u3067\u3042\u308b\u3053\u3068\u3092\u691c\u8a3c\u3059\u308b\u306e\u306f\u7c21\u5358\u3067\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {\\forall k \\in \\mathbb Z ,\\, a(x_0+bk)+b(y_0-ak)=ax_0+by_0=1} $$<\/div><\/dd><\/dl><p>\u3053\u308c\u304b\u3089\u306f\u3001\u3053\u308c\u3089\u306e\u30ab\u30c3\u30d7\u30eb\u3060\u3051\u304c\u89e3\u6c7a\u7b56\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30ab\u30c3\u30d7\u30eb (x, y) \u304c\u65b9\u7a0b\u5f0f\u306e\u89e3\u3067\u3042\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3057\u3087\u3046\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u79c1\u305f\u3061\u306f<\/p><dl><dd><div class=\"math-formual notranslate\">$$ {(1):\\qquad ax+by=1=ax_0+by_0} $$<\/div><\/dd><\/dl><p>\u7528\u8a9e\u3092\u5225\u306e\u65b9\u6cd5\u3067\u518d\u30b0\u30eb\u30fc\u30d7\u5316\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {(2):\\qquad a(x-x_0)=-b(y-y_0)} $$<\/div><\/dd><\/dl><p>\u3057\u305f\u304c\u3063\u3066\u3001\u6574\u6570 b \u306f\u7a4d a(x &#8211; x <sub>0<\/sub> ) \u3092\u9664\u7b97\u3057\u307e\u3059\u3002 a \u3068 b \u306f\u4e92\u3044\u306b\u7d20\u3067\u3042\u308b\u305f\u3081\u3001\u30ac\u30a6\u30b9\u306e\u88dc\u984c\u306b\u3088\u308a\u3001 b \u306f x &#8211; x <sub>0<\/sub>\u3092\u9664\u7b97\u3059\u308b\u3068\u8a00\u3048\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001x &#8211; x <sub>0<\/sub> = kb \u3068\u306a\u308b\u3088\u3046\u306a\u76f8\u5bfe\u6574\u6570 k \u304c\u5b58\u5728\u3057\u307e\u3059\u3002\u3042\u308b\u3044\u306f\u3082\u3046\u4e00\u5ea6<\/p><dl><dd><div class=\"math-formual notranslate\">$$ {(3):\\qquad x=x_0+kb} $$<\/div><\/dd><\/dl><p> (2) \u3067 x &#8211; x <sub>0 \u3092<\/sub>kb \u306b\u7f6e\u304d\u63db\u3048\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {(4) \\qquad akb=-b(y-y_0)} $$<\/div><\/dd><\/dl><p>\u6b21\u306b -b \u3067\u7c21\u7565\u5316\u3057\u307e\u3059<\/p><dl><dd><div class=\"math-formual notranslate\">$$ {(5) \\qquad y-y_0=-ak} $$<\/div><\/dd><\/dl><p>\u3042\u308b\u3044\u306f\u3082\u3046\u4e00\u5ea6<\/p><dl><dd><div class=\"math-formual notranslate\">$$ {(6) \\qquad y=y_0-ak} $$<\/div><\/dd><\/dl><p>\u3057\u305f\u304c\u3063\u3066\u3001(x,y) \u304c (1) \u306e\u89e3\u3067\u3042\u308b\u5834\u5408\u3001(x,y) = (x <sub>0<\/sub> +bk, y <sub>0<\/sub> &#8211; ak) \u3068\u306a\u308b\u76f8\u5bfe\u6574\u6570 k \u304c\u5b58\u5728\u3057\u307e\u3059\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u30c7\u30a3\u30aa\u30d5\u30a1\u30f3\u30c8\u30b9\u65b9\u7a0b\u5f0f ax+by = c - \u5b9a\u7fa9\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/YF-mOqEethk\/0.jpg\" style=\"width:100%;\"\/><\/figure><h3><span>\u65b9\u7a0b\u5f0f ax + by = c \u3053\u3053\u3067\u3001a \u3068 b \u306f\u4e92\u3044\u306b\u7d20\u3067\u3059<\/span><\/h3><p>\u7279\u5b9a\u306e\u89e3\u306f\u3001\u65b9\u7a0b\u5f0f ax + by = 1 \u306e\u7279\u5b9a\u306e\u89e3\u306b c \u3092\u639b\u3051\u308b\u3053\u3068\u3067\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u5b9f\u969b\u3001(x <sub>0<\/sub> , y <sub>0<\/sub> ) \u304c ax <sub>0<\/sub> + by <sub>0<\/sub> = 1 \u3092\u6e80\u305f\u3059\u5834\u5408\u3001ax <sub>0<\/sub> c + by <sub>0<\/sub> c = c\u3001\u5bfe (x <sub>0<\/sub> c, y <sub>0<\/sub> c) \u306f\u3001\u65b9\u7a0b\u5f0f ax + by = c \u306e\u89e3\u306b\u306a\u308a\u307e\u3059\u3002<\/p><p>\u524d\u3068\u540c\u69d8\u306e\u63a8\u8ad6\u306b\u3088\u308a\u3001\u3059\u3079\u3066\u306e\u89e3\u6c7a\u7b56\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002<\/p><div><p><strong>\u89e3\u306e\u30bb\u30c3\u30c8<\/strong><span>\u2014<\/span>\u7279\u5b9a\u306e\u89e3 (x <sub>1<\/sub> , y <sub>1<\/sub> ) \u304c\u65e2\u77e5\u3067\u3042\u308b\u5834\u5408\u3001\u89e3\u306e\u30bb\u30c3\u30c8\u306f\u30da\u30a2 (x <sub>1<\/sub> +bk, y <sub>1<\/sub> &#8211; ak) \u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002\u3053\u3053\u3067\u3001k \u306f\u4efb\u610f\u306e\u76f8\u5bfe\u6574\u6570\u3067\u3059\u3002<\/p><\/div><h3><span>\u4e00\u822c\u7684\u306a\u5834\u5408<\/span><\/h3><p>d \u3092 a \u3068 b \u306e gcd \u3068\u547c\u3073\u307e\u3059\u3002<\/p><div><p> <strong>c \u304c d \u306e\u500d\u6570\u3067\u306a\u3044\u5834\u5408<\/strong><span>\u2014<\/span>\u65b9\u7a0b\u5f0f\u306b\u306f\u89e3\u304c\u3042\u308a\u307e\u305b\u3093\u3002<\/p><\/div><p>\u78ba\u304b\u306b\u3001d \u3067 a \u3068 b \u3092\u5272\u308b\u3068\u3001d \u306f ax + \u306e\u5f62\u5f0f\u306e\u5f0f\u3067\u3082\u9664\u7b97\u3055\u308c\u307e\u3059\u3002\u3053\u3053\u3067\u3001a \u3068 b \u306f\u76f8\u5bfe\u7684\u306a\u6574\u6570\u3067\u3042\u308b\u305f\u3081\u3001d \u306f c \u3092\u9664\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p><p>\u3053\u3053\u3067\u3001d \u304c c \u3092\u9664\u7b97\u3059\u308b\u3068\u3001a <sub>1<\/sub> \u3001b <sub>1<\/sub> \u3001\u304a\u3088\u3073 c <sub>1<\/sub>\u306b\u5bfe\u3057\u3066\u6b21\u306e\u3088\u3046\u306a 3 \u3064\u306e\u6574\u6570\u304c\u5b58\u5728\u3059\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002<\/p><dl><dd> a = \u30c0<sub>1<\/sub><\/dd><dd> b = \u30c7\u30b7\u30d9\u30eb<sub>1<\/sub><\/dd><dd> c = \u76f4\u6d41<sub>1<\/sub><\/dd><\/dl><p> a <sub>1<\/sub>\u3068 b <sub>1<\/sub>\u306f\u4e92\u3044\u306b\u7d20\u3067\u3059\u3002<\/p><p>\u65b9\u7a0b\u5f0f ax + by = c \u306f\u3001a <sub>1<\/sub>\u3068 b <sub>1<\/sub>\u304c\u4e92\u3044\u306b\u7d20\u3067\u3042\u308b\u65b9\u7a0b\u5f0f a <sub>1<\/sub> x + b <sub>1<\/sub> y = c <sub>1<\/sub>\u3068\u7b49\u4fa1\u3067\u3042\u308a\u3001\u3053\u306e\u30b1\u30fc\u30b9\u306f\u3059\u3067\u306b\u89e3\u6c7a\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u6b21\u306b\u3001\u4e00\u822c\u7684\u306a\u5834\u5408\u306e\u89e3\u6c7a\u7b56\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002<\/p><dl><dd>\u7279\u5b9a\u306e\u89e3\uff08\uff58 <sub>\uff11<\/sub> \u3001\uff59 <sub>\uff11<\/sub> \uff09\u304c\u77e5\u3089\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u89e3\u306e\u30bb\u30c3\u30c8\u306f\u30da\u30a2\uff08\uff58 <sub>\uff11<\/sub> \uff0b\uff42 <sub>\uff11<\/sub> \uff4b\u3001\uff59 <sub>\uff11<\/sub> \u2212\uff41 <sub>\uff11<\/sub> \uff4b\uff09\u3067\u5f62\u6210\u3055\u308c\u3001\uff4b\u306f\u4efb\u610f\u306e\u76f8\u5bfe\u6574\u6570\u3067\u3042\u308b\u3002<\/dd><\/dl><p>\u3057\u305f\u304c\u3063\u3066\u3001\u30d7\u30ed\u30d1\u30c6\u30a3\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p><div><p> <strong>c \u304c d \u306e\u500d\u6570\u306e\u5834\u5408<\/strong><span>\u2014<\/span>\u3053\u306e\u65b9\u7a0b\u5f0f\u306b\u306f\u5e38\u306b\u89e3\u304c\u8a8d\u3081\u3089\u308c\u307e\u3059\u3002\u7279\u5b9a\u306e\u89e3 (x <sub>1<\/sub> , y <sub>1<\/sub> ) \u304c\u65e2\u77e5\u3067\u3042\u308b\u5834\u5408\u3001\u89e3\u306e\u30bb\u30c3\u30c8\u306f\u30da\u30a2\u3067\u5f62\u6210\u3055\u308c\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\left(x_1+ \\frac{bk}{d}; y_1 &#8211; \\frac{ak}{d}\\right)} $$<\/div>\u3053\u3053\u3067\u3001k \u306f\u4efb\u610f\u306e\u76f8\u5bfe\u6574\u6570\u3067\u3059\u3002<\/p><\/div><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u30c7\u30a3\u30aa\u30d5\u30a1\u30f3\u30c8\u30b9\u65b9\u7a0b\u5f0f ax+by = c - \u5b9a\u7fa9\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/xJtOFX9rJGA\/0.jpg\" style=\"width:100%;\"\/><\/figure><h3><span>\u6700\u5c0f\u9650\u306e\u30b7\u30b9\u30c6\u30e0<\/span><\/h3><p>\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001c \u304c d \u306e\u500d\u6570\u3067\u3042\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002<span>\u4e0e\u3048\u3089\u308c\u305f<\/span>\u65b9\u7a0b\u5f0f ax + by = c \u306e\u3059\u3079\u3066\u306e\u89e3\u306e\u4e2d\u3067\u3001 <span><i>x<\/i> <sup>2<\/sup> + <i>y<\/i> <sup>2<\/sup><\/span>\u304c\u53ef\u80fd\u306a\u9650\u308a\u6700\u5c0f\u3068\u306a\u308b\u3082\u306e\u3092\u63a2\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p><p>\u3053\u308c\u306b\u306f\u3001\u5024<span>( <i>x<\/i> <sub>1<\/sub> + <i>b<\/i> <sub>1<\/sub> <i>k<\/i> ) <sup>2<\/sup> + ( <i>y<\/i> <sub>1<\/sub> \u2212 <i>a<\/i> <sub>1<\/sub> <i>k<\/i> ) <sup>2<\/sup>\u3092<\/span>\u6700\u5c0f\u306b\u3059\u308b\u3053\u3068\u304c\u542b\u307e\u308c\u307e\u3059\u3002 <span><i>f<\/i> ( <i>t<\/i> ) = ( <i>x<\/i> <sub>1<\/sub> + <i>b<\/i> <sub>1<\/sub> <i>t<\/i> ) <sup>2<\/sup> + ( <i>y<\/i> <sub>1<\/sub> \u2212 <i>a<\/i> <sub>1<\/sub> <i>t<\/i> ) <sup>2<\/sup><\/span>\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u5b9f<span><a href=\"https:\/\/science-hub.click\/?p=72623\">\u5909\u6570<\/a><\/span>t \u306e\u95a2\u6570\u3092\u8003\u616e\u3059\u308b\u3068\u3001\u3053\u306e 2<span>\u6b21<\/span>\u95a2\u6570\u306e\u7814\u7a76\u306b\u3088\u308a\u3001\u3053\u306e\u95a2\u6570\u304c\u6b21\u306e\u3088\u3046\u306a\u6027\u8cea\u3092\u6301\u3064\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u6700\u5c0f\u5024<\/p><dl><dd><div class=\"math-formual notranslate\">$$ {t=\\frac{a_1y_1-b_1x_1}{a_1^2+b_1^2}} $$<\/div><\/dd><\/dl><p> t \u304c\u6574\u6570\u306e\u5834\u5408\u3001\u89e3\u306e\u30da\u30a2\u306f<span>( <i>x<\/i> <sub>1<\/sub> + <i>b<\/i> <sub>1<\/sub> <i>t<\/i> , <i>y<\/i> <sub>1<\/sub> \u2212 <i>a<\/i> <sub>1<\/sub> <i>t<\/i> )<\/span>\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u308c\u4ee5\u5916\u306e\u5834\u5408\u3001 <i>f \u3092<\/i>\u6700\u5c0f\u306b\u3059\u308b\u6574\u6570\u306f\u3001t \u306b\u8fd1\u3044\u6574\u6570 k le(s) \u306b\u306a\u308a\u307e\u3059\u3002<\/p><p> <span><i>x<\/i> <sup>2<\/sup> + <i>y<\/i> <sup>2<\/sup><\/span>\u306e\u5024\u304c\u6700\u5c0f\u3067\u3042\u308b ax + by = c \u306e\u89e3\u306e\u6574\u6570\u306e\u30da\u30a2\u306f<span>( <i>x<\/i> <sub>1<\/sub> + <i>b<\/i> <sub>1<\/sub> <i>k<\/i> , <i>y<\/i> <sub>1<\/sub> \u2212 <i>a<\/i> <sub>1<\/sub> <i>k<\/i> )<\/span>\u3067\u3059\u3002\u3053\u3053\u3067\u3001k \u306f\u6574\u6570( s) \u306b\u6700\u3082\u8fd1\u3044 k <div class=\"math-formual notranslate\">$$ {t=\\frac{a_1y_1-b_1x_1}{a_1^2+b_1^2}} $$<\/div> \u3002<\/p><p> a \u3068 b \u304c\u4e92\u3044\u306b\u7d20\u3067\u3042\u308b\u5834\u5408\u3001t \u304c\u6574\u6570\u3067\u3042\u308b\u5834\u5408\u3092\u8aac\u660e\u3059\u308b\u4fa1\u5024\u304c\u3042\u308a\u307e\u3059\u3002\u6574\u6570 c \u304c<span><i>a<\/i> <sup>2<\/sup> + <i>b<\/i> <sup>2<\/sup><\/span>\u306e\u500d\u6570\u3067\u3042\u308b\u5834\u5408\u306b\u9650\u308a\u3001t \u304c\u6574\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3059\u3002\u6700\u5c0f\u30b7\u30b9\u30c6\u30e0\u306e\u89e3\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ { \\left(\\frac{ac}{a^2+b^2},\\frac{bc}{a^2+b^2}\\right)} $$<\/div> \u3002<\/p><p> a \u3068 b \u304c\u4e92\u3044\u306b\u7d20\u3067\u3042\u308b\u5834\u5408\u3001a \u3068 b \u304c\u5947\u6570\u3067\u3042\u308a\u3001\u6574\u6570 c \u304c<div class=\"math-formual notranslate\">$$ {\\frac{a^2+b^2}{2}} $$<\/div><\/p><\/div><h2 class=\"ref_link\">\u53c2\u8003\u8cc7\u6599<\/h2><ol><li><a class=\"notranslate\" href=\"https:\/\/ar.wikipedia.org\/wiki\/%D9%85%D8%B9%D8%A7%D8%AF%D9%84%D8%A9_%D8%AF%D9%8A%D9%88%D9%81%D8%A7%D9%86%D8%AA%D8%A7%D9%8A%D9%86_ax_%2B_by_%3D_c\">\u0645\u0639\u0627\u062f\u0644\u0629 \u062f\u064a\u0648\u0641\u0627\u0646\u062a\u0627\u064a\u0646 ax + by = c \u2013 arabe<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/af.wikipedia.org\/wiki\/Vergelyking_(wiskunde)\">Vergelyking (wiskunde) \u2013 afrikaans<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/als.wikipedia.org\/wiki\/Gleichung\">Gleichung \u2013 al\u00e9manique<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/an.wikipedia.org\/wiki\/Ecuaci%C3%B3n\">Ecuaci\u00f3n \u2013 aragonais<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/anp.wikipedia.org\/wiki\/%E0%A4%B8%E0%A4%AE%E0%A5%80%E0%A4%95%E0%A4%B0%E0%A4%A3\">\u0938\u092e\u0940\u0915\u0930\u0923 \u2013 angika<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/ar.wikipedia.org\/wiki\/%D9%85%D8%B9%D8%A7%D8%AF%D9%84%D8%A9_%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A9\">\u0645\u0639\u0627\u062f\u0644\u0629 \u0631\u064a\u0627\u0636\u064a\u0629 \u2013 arabe<\/a><\/li><\/ol><\/div>\n<div class=\"feature-video\">\n <h2>\n  \u30c7\u30a3\u30aa\u30d5\u30a1\u30f3\u30c8\u30b9\u65b9\u7a0b\u5f0f ax+by = c &#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=\"\u3010\u88cf\u6280\u3011\u5408\u540c\u5f0f(mod)\u3067\u4e00\u6b21\u4e0d\u5b9a\u65b9\u7a0b\u5f0f\u3092\u4e00\u77ac\u3067\u89e3\u304f\u65b9\u6cd5\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/r0wRwNj_g58?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 \u65b9\u7a0b\u5f0f ax + by = c (\u4fc2\u6570 a\u3001b\u3001c \u306f 3 \u3064\u306e\u76f8\u5bfe\u6574\u6570\u3001\u672a\u77e5\u6570 x \u3068 y \u306f\u76f8\u5bfe\u6574\u6570) \u306f\u3001\u89e3\u304f\u306e\u304c\u6700\u3082\u7c21\u5358\u306a\u30c7\u30a3\u30aa\u30d5\u30a1\u30f3\u30c8\u30b9\u65b9\u7a0b\u5f0f\u306e 1 \u3064\u3067\u3059\u3002\u305d\u306e\u89e3\u6c7a\u7b56\u306f\u3001 Euclid\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3001 B [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":100750,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/img.youtube.com\/vi\/8X2Wu-fWCmE\/0.jpg","fifu_image_alt":"\u30c7\u30a3\u30aa\u30d5\u30a1\u30f3\u30c8\u30b9\u65b9\u7a0b\u5f0f ax+by = c - \u5b9a\u7fa9","footnotes":""},"categories":[5],"tags":[31886,88037,36947,11,13,10,14,12,8,3944,16,88036,15,9],"class_list":["post-100749","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dictionary","tag-by","tag-hotel-des-tournelles","tag-diophantienne","tag-techniques","tag-technologie","tag-actualite","tag-news","tag-dossier","tag-definition","tag-equation","tag-sciences","tag-membranaires","tag-article","tag-explications"],"_links":{"self":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/100749"}],"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=100749"}],"version-history":[{"count":0,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/100749\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/media\/100750"}],"wp:attachment":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=100749"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=100749"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=100749"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}