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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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