MathDB
3 perfect squares

Source: JOM 2024 P5

February 29, 2024
number theory

Problem Statement

Do there exist infinitely many triplets of positive integers (a,b,c)(a, b, c) such that the following two conditions hold: 1. gcd⁡(a,b,c)=1\gcd(a, b, c) = 1; 2. a+b+c,a2+b2+c2a+b+c, a^2+b^2+c^2 and abcabc are all perfect squares?
(Proposed by Ivan Chan Guan Yu)
Back to ProblemsView on AoPS