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PHP : Function Reference : GMP Functions : gmp_gcdext

gmp_gcdext

Calculate GCD and multipliers (PHP 4 >= 4.0.4, PHP 5)
array gmp_gcdext ( resource a, resource b )

Example 792. 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
?>

Code Examples / Notes » gmp_gcdext

fatphil

The extended GCD can be used to calculate mutual modular inverses of two
coprime numbers. Internally gmp_invert uses this extended GCD routine,
but effectively throws away one of the inverses.
If gcd(a,b)=1, then r.a+s.b=1
Therefore  r.a == 1 (mod s) and s.b == 1 (mod r)
Note that one of r and s will be negative, and so you'll want to
canonicalise it.


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