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a|b^3, b|c^3 , c|a^3 . Prove that abc|(a+b+c)^{13}

Source: CRMO 2012 region 1 p2

September 30, 2018

number theorydividesdivisiblepowers

Problem Statement

Let

a,b,c

be positive integers such that

a|b^3, b|c^3

and

c|a^3

. Prove that

abc|(a+b+c)^{13}