Given parameters $a,b,D$, all integers, I want to find all the integer solutions $(x,y)$ of
Or at least a nice way to characterize them. Also, for a given $R$, it is actually enough for me to find the solutions which also satisfy
(i.e. all the integer points in a some disc around the origin) but if the problem can be solved without using this additional constraint I'd be happy to hear how.