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Turkey NMO 2003 Problem 4

Source: Turkey NMO 2003 Problem 4

August 28, 2011

number theorygreatest common divisormodular arithmeticDiophantine equationnumber theory unsolved

Problem Statement

Suppose that

2^{2n+1}+ 2^{n}+1=x^{k}

, where

k\geq2

and

n

are positive integers. Find all possible values of

n