If $a,b,c$ are positive integers such that $b | a^3, c | b^3$ and $a | c^3$ , prove that $abc | (a+b+c)^{13}$
Problem
Source: Norwegian Mathematical Olympiad 1999 - Abel Competition p2b
Tags: divides, divisible, number theory
Source: Norwegian Mathematical Olympiad 1999 - Abel Competition p2b
Tags: divides, divisible, number theory
If $a,b,c$ are positive integers such that $b | a^3, c | b^3$ and $a | c^3$ , prove that $abc | (a+b+c)^{13}$