2014/15 AHSMC Part 1 Problem 9

Clearly $n \ne 1$, so that $m = \dfrac{n}{n-1} = 1 + \dfrac{1}{n-1}$. Since $m$ is an integer, we can only have $n = 0$ or $2$, with $m = 0$ and $2$ respectively. The answer is (C).