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Problem 4, Olympic Revenge 2013

Source: XII Olympic Revenge - 2013

January 26, 2013
modular arithmeticnumber theory proposednumber theory

Problem Statement

Find all triples (p,n,k)(p,n,k) of positive integers, where pp is a Fermat's Prime, satisfying pn+n=(n+1)kp^n + n = (n+1)^k.
Observation: a Fermat's Prime is a prime number of the form 2α+12^{\alpha} + 1, for α\alpha positive integer.
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