# Fermat Prime?

Find all triples $$(p,n,k)$$ of positive integers, where $$p$$ is a Fermat's Prime, satisfying

$\large{p^n + n = (n+1)^k}$

Observation: a Fermat's Prime is a prime number of the form $$2^{\alpha} + 1$$, for $$\alpha$$ positive integer.

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