2005 OIM Problems/Problem 3

Problem

Let $p$ greater than 3 be a prime number. If

\[\frac{1}{1^p}+\frac{1}{2^p}+\frac{1}{3^p}+\cdots+\frac{1}{(p-1)^p}=\frac{n}{m}\]

where the greatest common factor of $n$ and $m$ is 1, show that $p^3$ divides $n$.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions