MathDB

5

Part of 2001 USAMO

Problems(1)

USAMO 2001 Problem 5

Source:

9/30/2005
Let SS be a set of integers (not necessarily positive) such that (a) 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; (b) if xx and yy are elements of SS (possibly equal), then x2−yx^2-y also belongs to SS. Prove that SS is the set of all integers.
AMCUSAMOmodular arithmeticnumber theory