MathDB
O 6

Source:

May 25, 2007
modular arithmeticinduction

Problem Statement

Let SS be a set of integers such that [*] there exist a,b∈Sa, b \in S with gcd⁡(a,b)=gcd⁡(a−2,b−2)=1\gcd(a, b)=\gcd(a-2,b-2)=1, [*] if x,y∈Sx,y\in S, then x2−y∈Sx^2 -y\in S. Prove that S=ZS=\mathbb{Z}.
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