MathNet 2016-part-03 — 184 problems (EN–VI) Question 6

Let $m$ and $n$ be positive integers such that $m\gt n$. Define $x_k = \frac{m+k}{n+k}$ for $k=1,2,\ldots,n+1$. Prove that if $x_1,x_2,\ldots,x_{n+1}$ are integers, then $x_1x_2\ldots x_{n+1}-1$ is divisible by at least one odd prime.