Problem

Source: SMO 2011 Problem 2

Tags: number theory, greatest common divisor, number theory unsolved



If positive integers, $a,b,c$ are pair-wise co-prime, and, \[\ a^2|(b^3+c^3), b^2|(a^3+c^3), c^2|(a^3+b^3) \] find $a,b,$ and $c$