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A Divisibility Problem
04-29-2010, 12:25 PM (This post was last modified: 09-30-2010 09:32 AM by elim.)
Post: #1
A Divisibility Problem
Let $m,n$ be positive integers and $n>1, \; 2 \nmid m$. Let $r,s$ be positive integers such that

$\displaystyle{\frac{r}{s}=\sum_{k=0}^{2^n-1}\frac1{(2k+1)^m}}$

Prove that $2^{n+2}|r$

http://www.artofproblemsolving.com/Forum...8#p1859798
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