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Easy diophantine

Source: European Mathematical Cup 2012, Senior Division, Problem 1

July 27, 2013
number theoryprime numbersnumber theory proposed

Problem Statement

Find all positive integers aa, bb, nn and prime numbers pp that satisfy
a2013+b2013=pn. a^{2013} + b^{2013} = p^n\text{.}
Proposed by Matija Bucić.
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