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I need to find a good configuration for my computational kernel, which forces me to find some integer solutions to the following simple equation:
$a \cdot x - b \cdot y = c$,
where $a$, $b$ and $c$ are constant positive integers, and $x$ and $y$ are my unknown, that I need to also be positive integers.
I thought I could solve this using the Diophantine solution, but I'm not sure how to proceed due to one of the addends to be negative.
What is the best way to find all solutions to such an equation?