MathDB
USAMO 2001 Problem 5

Source:

September 30, 2005
AMCUSAMOmodular arithmeticnumber theory

Problem Statement

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.
Back to ProblemsView on AoPS