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if x | y^3 , y | z^3, z | x^3, and xyz | (x + y + z) ^n , find min n

Source: 2019 Austrian Federal Competition For Advanced Students, Part 2 p6

March 4, 2020

number theorydividesmin

Problem Statement

Find the smallest possible positive integer n with the following property: For all positive integers

x, y

and

z

with

x | y^3

and

y | z^3

and

z | x^3

always to be true that

xyz| (x + y + z) ^n

.
(Gerhard J. Woeginger)