Integer solution for $174582x + 1818342y = 54$

Question

How can I find an integer solution for $x$ and $y$ for this problem type?

I think I have to find a modulo relation between $54, 174582$ and $1818342$, but I am clueless.

Answer 1

Since $54$ is the gcd of $174582$ and $1818342$, we can use the Extended Euclidean algorithm.