\ubcf8 \uac15\uc88c\uc5d0\uc11c\ub294 A, B, C\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c Ax + By = C\uc758 \uc815\uc218\ud574\ub97c \uad6c\ud558\ub294 \ubb38\uc81c\ub97c \ub2e4\ub8f9\ub2c8\ub2e4.<\/p>\n<\/header>\n \uc8fc\uc5b4\uc9c4 \uc815\uc218 A, B, C\uc5d0 \ub300\ud574 Ax + By = C\ub97c \ub9cc\uc871\ud558\ub294 \ubaa8\ub4e0 \uc815\uc218 \uc30d (x, y)\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \uc608\ub97c \ub4e4\uc5b4, A = 2, B = 3, C = 6\uc758 \uacbd\uc6b0, \uac00\ub2a5\ud55c \ud574\ub294 (0, 2), (3, 0), (1, 1) \ub4f1\uc785\ub2c8\ub2e4. \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud574 \uba3c\uc800 \ubb38\uc81c\ub97c \ubd84\uc11d\ud574\ubcf4\uba74, \uc8fc\uc5b4\uc9c4 \uc2dd Ax + By = C\ub294 x\uc640 y\uc758 \uc870\ud569\uc744 \ucc3e\ub294 \uac83\uc785\ub2c8\ub2e4. \ubb38\uc81c\uc758 \ud574\ub97c \ucc3e\uae30 \uc704\ud574, \uba3c\uc800 C\uac00 A\uc640 B\uc758 \ucd5c\ub300\uacf5\uc57d\uc218(GCD)\uac00 \ub418\ub294\uc9c0\ub97c \ud655\uc778\ud574\uc57c \ud569\ub2c8\ub2e4. \uc5ec\uae30\uc11c x, y\ub294 \uc815\uc218\uc785\ub2c8\ub2e4. \uc774 \uc2dd\uc744 \ubcc0\ud615\ud558\uc5ec \uc815\uc218\ud574\ub97c \ucc3e\uc744 \uc218 \uc788\uc74c\uc744 \uc54c \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n \uc774\uc81c \uc704\uc758 \ub17c\ub9ac\ub97c \ubc14\ud0d5\uc73c\ub85c \uc790\ubc14\ub97c \uc0ac\uc6a9\ud558\uc5ec \ud504\ub85c\uadf8\ub7a8\uc744 \uad6c\ud604\ud574\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc704 \ucf54\ub4dc\ub294 \ub450 \uc218 a, b\uc758 \ucd5c\ub300\uacf5\uc57d\uc218\ub97c \uacc4\uc0b0\ud558\ub294 Euclid \uc54c\uace0\ub9ac\uc998\uc744 \uc774\uc6a9\ud55c \ud568\uc218\uc785\ub2c8\ub2e4.<\/p>\n \uc704 \ucf54\ub4dc\ub97c \uc0ac\uc6a9\ud558\uc5ec \ub2e4\uc591\ud55c \uc870\ud569\uc758 A, B, C\uc5d0 \ub300\ud574 \ud574\ub97c \ucc3e\uc744 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc774\ubc88 \uac15\uc88c\uc5d0\uc11c\ub294 Ax + By = C\uc758 \uc815\uc218\ud574\ub97c \uad6c\ud558\ub294 \ubc29\ubc95\uc5d0 \ub300\ud574 \uc0b4\ud3b4\ubcf4\uc558\uc2b5\ub2c8\ub2e4.\ubb38\uc81c \uc124\uba85<\/h2>\n
\n \uc774\ub54c A, B, C\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \uc870\uac74\uc744 \ub9cc\uc871\ud569\ub2c8\ub2e4:<\/p>\n\n
\n \uadf8\ub7ec\ub098, \ud574\uac00 \ubb34\ud55c\ud788 \uc874\uc7ac\ud558\ub294 \uacbd\uc6b0\ub3c4 \uc788\uc73c\uba70, \ud574\uac00 \uc874\uc7ac\ud558\uc9c0 \uc54a\uc744 \ub54c\ub3c4 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n<\/section>\n\ubb38\uc81c \ud480\uc774 \uacfc\uc815<\/h2>\n
1. \ubb38\uc81c \ubd84\uc11d<\/h3>\n
\n A\uc640 B\uc758 \ubd80\ud638\uc5d0 \ub530\ub77c \uac00\ub2a5\ud55c \ud574\uc758 \uac1c\uc218\uc640 \ubc94\uc704\uac00 \ub2ec\ub77c\uc9d1\ub2c8\ub2e4.
\n \uc608\ub97c \ub4e4\uc5b4, A\uc640 B \ubaa8\ub450 0\uc778 \uacbd\uc6b0\ub294 \uc608\uc678\ub85c, \uadf8 \uc678\uc758 \uacbd\uc6b0\ub294 \ub450 \ubcc0\uc218 \uc911 \ud558\ub098\uac00 \ub2e4\ub978 \ubcc0\uc218\ub97c \uae30\uc900\uc73c\ub85c \uc5b4\ub5bb\uac8c \ubcc0\ud560 \uc218 \uc788\ub294\uc9c0\ub97c \ud30c\uc545\ud558\ub294 \uac83\uc774 \uc911\uc694\ud569\ub2c8\ub2e4.<\/p>\n2. \ud574\uc758 \uac1c\uc218 \uacc4\uc0b0<\/h3>\n
\n GCD\uac00 C\uc758 \uc57d\uc218\uac00 \uc544\ub2c8\uba74 \ud574\ub294 \uc874\uc7ac\ud558\uc9c0 \uc54a\uc73c\ub2c8, GCD\ub97c \uc774\uc6a9\ud574 \uac04\ub7b5\ud558\uac8c \uc544\ub798\uc640 \uac19\uc774 \uc124\uba85\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n\n gcd(a, b) = ax + by\n <\/pre>\n
3. \uc790\ubc14 \uad6c\ud604<\/h3>\n
\n \uac01 \ub2e8\uacc4\uc5d0 \ub300\ud574 \uc124\uba85\ud558\uace0, \ucf54\ub4dc\ub3c4 \ud3ec\ud568\ud558\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n3.1. \ucd5c\ub300\uacf5\uc57d\uc218 (GCD) \uacc4\uc0b0 \ud568\uc218<\/h4>\n
\npublic static int gcd(int a, int b) {\n while (b != 0) {\n int temp = b;\n b = a % b;\n a = temp;\n }\n return a;\n}\n <\/code><\/pre>\n3.2. \ud574 \ucc3e\uae30 \ubc0f \ucd9c\ub825 \ud568\uc218<\/h4>\n
\npublic static void findSolutions(int A, int B, int C) {\n \/\/ GCD \uacc4\uc0b0\n int gcdAB = gcd(Math.abs(A), Math.abs(B));\n \n \/\/ C\uac00 GCD\uc758 \ubc30\uc218\uc778\uc9c0 \ud655\uc778\n if (C % gcdAB != 0) {\n System.out.println(\"\ud574\uac00 \uc5c6\uc2b5\ub2c8\ub2e4.\");\n return;\n }\n\n \/\/ x,y \uacc4\uc0b0 \ub85c\uc9c1\n int x = C \/ A;\n int y = 0; \/\/ \ucd08\uae30 y \uac12\n \/\/ \ud574 \ucd9c\ub825\n System.out.println(\"\uac00\ub2a5\ud55c \ud574: x = \" + x + \", y = \" + y);\n \/\/ \ub610\ub294 \ubc18\ubcf5\ubb38\uc744 \uc0ac\uc6a9\ud558\uc5ec \ub2e4\ub978 \ud574 \ucd9c\ub825 \uac00\ub2a5\n}\n <\/code><\/pre>\n4. \uc804\uccb4 \ucf54\ub4dc<\/h3>\n
\npublic class LinearEquationSolver {\n public static int gcd(int a, int b) {\n while (b != 0) {\n int temp = b;\n b = a % b;\n a = temp;\n }\n return a;\n }\n\n public static void findSolutions(int A, int B, int C) {\n int gcdAB = gcd(Math.abs(A), Math.abs(B));\n if (C % gcdAB != 0) {\n System.out.println(\"\ud574\uac00 \uc5c6\uc2b5\ub2c8\ub2e4.\");\n return;\n }\n\n \/\/ Fixed-point iteration for solution finding\n for (int x = -1000; x <= 1000; x++) {\n if ((C - A * x) % B == 0) {\n int y = (C - A * x) \/ B;\n System.out.println(\"\uac00\ub2a5\ud55c \ud574: x = \" + x + \", y = \" + y);\n }\n }\n }\n\n public static void main(String[] args) {\n findSolutions(2, 3, 6);\n \/\/ \ucd94\uac00 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\n findSolutions(1, -1, 0);\n }\n}\n <\/code><\/pre>\n
\n \ud574\ub97c \ucd9c\ub825\ud558\ub294 \ubd80\ubd84\uc740 \uc9c1\uc811 \ubc18\ubcf5\ubb38\uc744 \ud1b5\ud574 \ucc3e\ub294 \ubc29\uc2dd\uc774\uba70,
\n \ubcf4\ud1b5 \uc218\uac00 \uc801\uc744 \uacbd\uc6b0 \ub354 \ube60\ub978 \uacb0\uacfc\ub97c \ubcf4\uc5ec\uc90d\ub2c8\ub2e4.<\/p>\n<\/section>\n\ub9c8\ubb34\ub9ac \ubc0f \uc694\uc57d<\/h2>\n
\n GCD\ub97c \uc0ac\uc6a9\ud558\uc5ec \ud574\uac00 \uc874\uc7ac\ud558\ub294\uc9c0\ub97c \ud310\ubcc4\ud558\uace0, \ubc18\ubcf5\ubb38\uc744 \uc0ac\uc6a9\ud558\uc5ec \uac00\ub2a5\ud55c \ud574\ub97c \ucd9c\ub825\ud558\ub294 \uae30\ubcf8\uc801\uc778 \ubc29\uc2dd\uc5d0 \ub300\ud574 \uc124\uba85\ud588\uc2b5\ub2c8\ub2e4.
\n \uc774\ub7ec\ud55c \uae30\ubc95\uc740 \ub2e4\uc591\ud55c \ubb38\uc81c\uc5d0 \uc751\uc6a9\ub420 \uc218 \uc788\uc73c\uba70, \uc54c\uace0\ub9ac\uc998\uc758 \uc2ec\ud654 \ud559\uc2b5\uc5d0 \ud070 \ub3c4\uc6c0\uc774 \ub420 \uac83\uc785\ub2c8\ub2e4.<\/p>\n<\/section>\n