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Azerbaijan IMO TST

Source:

September 15, 2015
number theory

Problem Statement

Let nn and kk be two positive integers such that n>kn>k. Prove that the equation xn+yn=zkx^n+y^n=z^k has a solution in positive integers if and only if the equation xn+yn=znāˆ’kx^n+y^n=z^{n-k} has a solution in positive integers.
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