# gmp_gcdext

## Calculate GCD and multipliers (PHP 4 >= 4.0.4, PHP 5) array gmp_gcdext ( resource a, resource b )

Calculates g, s, and t, such that ```a*s + b*t = g = gcd(a,b)```, where gcd is the greatest common divisor. Returns an array with respective elements g, s and t.

This function can be used to solve linear Diophantine equations in two variables. These are equations that allow only integer solutions and have the form: `a*x + b*y = c`. For more information, go to the » "Diophantine Equation" page at MathWorld

### 例 674. Solving a linear Diophantine equation

```<?php // Solve the equation a*s + b*t = g // where a = 12, b = 21, g = gcd(12, 21) = 3 \$a = gmp_init(12); \$b = gmp_init(21); \$g = gmp_gcd(\$a, \$b); \$r = gmp_gcdext(\$a, \$b); \$check_gcd = (gmp_strval(\$g) == gmp_strval(\$r['g'])); \$eq_res = gmp_add(gmp_mul(\$a, \$r['s']), gmp_mul(\$b, \$r['t'])); \$check_res = (gmp_strval(\$g) == gmp_strval(\$eq_res)); if (\$check_gcd && \$check_res) {    \$fmt = "Solution: %d*%d + %d*%d = %d\n";    printf(\$fmt, gmp_strval(\$a), gmp_strval(\$r['s']), gmp_strval(\$b),    gmp_strval(\$r['t']), gmp_strval(\$r['g'])); } else {    echo "Error while solving the equation\n"; }     // output: Solution: 12*2 + 21*-1 = 3 ?>```