GMP_GCDEXT(3)								 1							     GMP_GCDEXT(3)

gmp_gcdext - Calculate GCD and multipliers

SYNOPSIS

       array gmp_gcdext (GMP  $a, GMP  $b)

DESCRIPTION

	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

	      o $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.

	      o $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) {
		  $fmt = "Solution: %d*%d + %d*%d = %d
";
		  printf($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
";
	      }

	      // output: Solution: 12*2 + 21*-1 = 3
	      ?>

PHP Documentation Group 													     GMP_GCDEXT(3)