   #PHP Manual GMP functions gmp_gcd gmp_hamdist

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                                  gmp_gcdext

   (PHP 4 >= 4.0.4)
   gmp_gcdext -- Calculate 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

   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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