Diophantic linear Equations

The simplest linear Diophantine equation takes the form

,

where a, b and c are given integers, x, y — unknowns.

The solutions are completely described by the following theorem: This Diophantine equation has a solution (where x and y are integers) if and only if c is a multiple of the greatest common divisor of a and b. Moreover, if (x, y) is a solution, then the other solutions have the form (x + kv, y - ku), where k is an arbitrary integer, and u and v are the quotients of a and b (respectively) by the greatest common divisor of a and b.To find the solution one can use Extended Euclidean algorithm (except for a = b = 0 where either there are unlimited number of solutions or none).

Mathcad has a gcd function that will determine greatest common divisor.  gcd(a,b)

You can determine if c is a multiple by testing the mod function for zero return. mod(c,gcd(a,b))=0 is pass

You could program to search for them.