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When is (a+b+c)^13 divisible by abc?

Source: Poland Math Olympiad 1993 Round 1 #8

June 3, 2023

Problem Statement

Given positive integers a,b,ca,b,c such that a3a^3 is divisible by bb, b3b^3 is divisible by cc, c3c^3 is divisible by aa. Prove that (a+b+c)13(a+b+c)^{13} is divisible by abcabc.
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