# gmp_gcdext

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

gmp_gcdextCalculate GCD and multipliers

### Description

array gmp_gcdext ( GMP \$a , GMP \$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

### 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']));
\$check_res = (gmp_strval(\$g) == gmp_strval(\$eq_res));

if (
\$check_gcd && \$check_res) {

\$fmt "Solution: %d*%d + %d*%d = %d\n";

printf(\$fmtgmp_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
?>