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a|b^4, b|c^4 , c|a^4 . Prove that abc|(a+b+c)^{21}

Source: CRMO 2012 Region 2 p2

September 30, 2018

number theorydividesdivisiblepowers

Problem Statement

Let

a,b,c

be positive integers such that

a|b^4, b|c^4

and

c|a^4

. Prove that

abc|(a+b+c)^{21}