Question 152
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 all the numbers $x_1, x_2, \ldots, x_{n+1}$ are integers,
then $x_1 x_2 \ldots x_{n+1} - 1$ is divisible by an odd prime.
(IMO-2015 Shortlist, Problem N3)
Prove that if all the numbers $x_1, x_2, \ldots, x_{n+1}$ are integers,
then $x_1 x_2 \ldots x_{n+1} - 1$ is divisible by an odd prime.
(IMO-2015 Shortlist, Problem N3)