Let $m$ and $n$ be positive integers such that $m>n$. Define $x_k=\frac{m+k}{n+k}$ for $k=1,2,\ldots,n+1$. Prove that if all the numbers $x_1,x_2,\ldots,x_{n+1}$ are integers, then $x_1x_2\ldots x_{n+1}-1$ is divisible by an odd prime.
\begin{flushright}\emph{(Austria)}\end{flushright}
Školjka 
and 
be positive integers such that 
. Define 
for 
. Prove that if all the numbers 
are integers, then 
is divisible by an odd prime.