The gmp_gcdext() is an inbuilt function in PHP which calculates the GCD ( Greatest Common Divisor ) and multipliers of a given equation such that
a * x + b * y = GCD(a, b), where GCD is the greatest common divisor.
This function is used to solve linear
Diophantine equation in two variables .
Syntax:
array gmp_gcdext ( GMP $a, GMP $b )
Parameters: The gmp_gcdext() function accepts two parameters as listed above and described below:
- $a: This parameter can be a GMP resource in PHP 5.5 and earlier, a GMP object in PHP 5.6, or we are also allowed to pass a numeric string provided that it is possible to convert that string to a number.
- $b: This parameter can be a GMP resource in PHP 5.5 and earlier, a GMP object in PHP 5.6, or we are also allowed to pass a numeric string provided that it is possible to convert that string to a number.
Return Values: This function will return an array of GMP numbers (
GNU Multiple Precision: For large numbers) that is the multipliers (x and y of a given equation ) and the gcd.
Examples:
Input: a = 12 , b = 21
equation = 12 * x + 21 * y = 3
Output:
Input: a = 5 , b = 10
equation = 5 * x + 10 * y = 5
Output: x = 1 , y = 0 , GCD(12,21) = 5
Below program illustrate the gmp_gcdext() function:
Output:
Solution: 5 * -1 + 6 * 1 = 1
Reference : https://www.php.net/manual/en/function.gmp-gcdext.php
