MathDB
Nice triples

Source:

October 22, 2010
arithmetic sequencenumber theory unsolvednumber theory

Problem Statement

Call a triple (a,b,c)(a, b, c) of positive integers a nice triple if a,b,ca, b, c forms a non-decreasing arithmetic progression, gcd(b,a)=gcd(b,c)=1gcd(b, a) = gcd(b, c) = 1 and the product abcabc is a perfect square. Prove that given a nice triple, there exists some other nice triple having at least one element common with the given triple.
Back to ProblemsView on AoPS