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Bosnia and Herzegovina TST 2001 Day 2 Problem 3

Source: Bosnia and Herzegovina Team Selection Test 2001

September 19, 2018
number theoryinfinitely many solutionsequation

Problem Statement

Prove that there exists infinitely many positive integers nn such that equation (x+y+z)3=n2xyz(x+y+z)^3=n^2xyz has solution (x,y,z)(x,y,z) in set N3\mathbb{N}^3
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