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b | a^3, c | b^3 , a | c^3 => abc | (a+b+c)^{13}

Source: Norwegian Mathematical Olympiad 1999 - Abel Competition p2b

February 11, 2020

dividesdivisiblenumber theory

Problem Statement

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}