I have the following equation:
$\frac{a + b x}{c} \in \mathbb{N}$ where $a,b,c,x \in \mathbb{N}$.
and I want to find all x that satisfy these requirements. This should be the same as:
$a + b x = c y,~~~ y \in \mathbb{N}$
This looks like a linear Diophantine equation, but Bézout's identity cannot be used since $a$ is not necessarily $\gcd(b, c)$.
How can I solve for $x$?