Question 117
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.
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.