# How Far Can You Go?

Find the sum of all positive integers $$n$$ such that there exists $$p\in \mathbb{N}$$ that satisfies the divisibility

$p^{n-1}+(p+2)^{n-1}\mid p^n+(p+2)^n.$

This problem is a generalization by me of a problem that appeared in St. Petersburg City Mathematical Olympiad 1996.

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