MathDB
system 3x3 in N^3 with LCM a^2 + b^2 = n lcm(a, b) + n^2 PMO 2019

Source: 21st Philippine Mathematical Olympiad 2019 p3 PMO

January 7, 2020
system of equationsnumber theoryleast common multiple

Problem Statement

Find all triples (a,b,c)(a, b, c) of positive integers such that a2+b2=n⋅lcm(a,b)+n2a^2 + b^2 = n\cdot lcm(a, b) + n^2 b2+c2=n⋅lcm(b,c)+n2b^2 + c^2 = n \cdot lcm(b, c) + n^2 c2+a2=n⋅lcm(c,a)+n2c^2 + a^2 = n \cdot lcm(c, a) + n^2 for some positive integer nn.
Back to ProblemsView on AoPS