# gmp_gcdext

(PHP 4 >= 4.0.4, PHP 5, PHP 7)

gmp_gcdext — Calculate GCD and multipliers

### Description

gmp_gcdext ( GMP `$a` , GMP `$b` ) : array

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

### Parameters

`a`

  Either a GMP number resource in PHP 5.5 and earlier, a GMP object in PHP 5.6 and later, or a numeric string provided that it is possible to convert the latter to a number.

`b`

  Either a GMP number resource in PHP 5.5 and earlier, a GMP object in PHP 5.6 and later, or a numeric string provided that it is possible to convert the latter to a number.

### Return Values

An array of GMP numbers.

### Examples

Example #1 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
?>`