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# gmp_gcdext

(PHP 4 >= 4.0.4, PHP 5)

gmp_gcdextCalculate GCD and multipliers

### Description

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

### Parameters

a

It can be either a GMP number resource, or a numeric string given that it is possible to convert the latter to a number.

b

It can be either a GMP number resource, or a numeric string given 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?>```

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