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If $x^n + y^n = p^k$, $n$ is a power of $p$ (Russia 1996)

Source: All-Russian Olympiad 1996, Grade 9, First Day, Problem 3

April 18, 2013
number theory proposednumber theory

Problem Statement

Let x,y,p,nx, y, p, n, and kk be positive integers such that xn+yn=pkx^n + y^n = p^k. Prove that if n>1n > 1 is odd, and pp is an odd prime, then nn is a power of pp.
A. Kovaldji, V. Senderov
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