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2016 Latvia National Olympiad 3rd Round Grade12Problem1

Source:

July 22, 2016
number theoryPerfect Powers

Problem Statement

Given that xx, yy and zz are positive integers such that x3y5z6x^3y^5z^6 is a perfect 7th power of a positive integer, show that also x5y6z3x^5y^6z^3 is a perfect 7th power.
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