How to solve Linear Diophantine equations in programming?

Question

I have read about Linear Diophantine equations such as ax+by=c are called diophantine equations and give an integer solution only if gcd(a,b) divides c

Answer 1

Solving Linear Diophantine equations

ax + by = c and gcd(a, b) divides c.

1. Divide a, b and c by gcd(a,b).
2. Now gcd(a,b) == 1
3. Find solution to aU + bV = 1 using Extended Euclidean algorithm
4. Multiply equation by c. Now you have a(Uc) + b (Vc) = c
5. You found solution x = U*c and y = V * c

Answer 2

The problem is that the input values are 64-bit (up to 10^18) so the LCM can be up to 128 bits large, therefore l can overflow. Since k is 64-bit, an overflowing l indicates k = 0 (so answer is 1). You need to check this case.

For instance:

unsigned long long l=g1/g; // cannot overflow
unsigned long long res;
if ((l * g2) / g2 != l)
{
    // overflow case - l*g2 is very large, so k/(l*g2) is 0
    res = 0;
}
else
{
    l *= g2;
    res = k / l;
}