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As the title says,

Find all positive integers $n$ for which $(n-1)!+1$ is a power of $n$.

The solutions I've found are $\{2,3,5\}$ (thanks Brandon!), but I'm having difficulties proving that these are the only ones. What I've got so far is that $n$ must be prime since $(n-1)!+1$ would not be congruent to $n$ if $n$ were composite.

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    $n=2,3$ are solutions as well.2011-12-18

2 Answers 2