I've been helping students with graphing linear equations in the standard form lately, and I was wanting to come up with a way to figure out what values we could put in for one variable and get an integer for the other.

We're looking at , where a,b,c are known integers.

Alternately,

So I need to find such that for all

I've never taken a number theory course, so please use an explanation that'll make sense to me. Thanks.