Let $S$ be a set of integers (not necessarily positive) such that (a) there exist $a,b \in S$ with $\gcd(a,b)=\gcd(a-2,b-2)=1$; (b) if $x$ and $y$ are elements of $S$ (possibly equal), then $x^2-y$ also belongs to $S$. Prove that $S$ is the set of all integers. MithsApprentice view topic 6