初等数论——整数的分解

已知a, b, c，求解a * x + b * y = c
int x_0, y_0;
int ext_gcd(int a, int b) {
if (b == 0) { x_0 = 1; y_0 = 0; return a; }
int gcd = ext_gcd(b, a % b);
int t = x_0; x_0 = y_0; y_0 = t - a / b * y_0;
return gcd;
}
int main() {
gcd = ext_gcd(a, b);
if (c % gcd == 0) {
x_0 *= c / gcd; y_0 *= c / gcd;
a_1 = a / gcd; b_1 = b / gcd;
x = x_0 - b_1 * t; y = y_0 + a_1 * t; \\t = 0, 1, -1, ...
}
return 0;
}