2005 OIM Problems/Problem 3
Problem
Let 
greater than 3 be a prime number. If
![\[\frac{1}{1^p}+\frac{1}{2^p}+\frac{1}{3^p}+\cdots+\frac{1}{(p-1)^p}=\frac{n}{m}\]](http://latex.artofproblemsolving.com/d/a/0/da0aea98bc5fb2b2b344a04047d9f8e94b0563f3.png)
where the greatest common factor of 
and 
is 1, show that 
divides .
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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