Question 5
Let $S\subseteq\mathbb Z$ satisfy:
(a) There exist $a,b\in S$ with $\gcd(a,b)=\gcd(a-2,b-2)=1$.
(b) If $x,y\in S$ (possibly equal), then $x^2-y\in S$.
Prove that $S=\mathbb Z$.
(a) There exist $a,b\in S$ with $\gcd(a,b)=\gcd(a-2,b-2)=1$.
(b) If $x,y\in S$ (possibly equal), then $x^2-y\in S$.
Prove that $S=\mathbb Z$.