2017/18 AHSMC Part 1 Problem 5

Since $\dfrac{p}{n}$ is an integer, $n \mid p$ and hence $n = 1$ or $n = p$. It follows that $p + 1$ is a perfect square, thus there is a positive integer $m$ such that $p + 1 = m^2$ or $p = (m - 1)(m + 1)$. Hence $1 = m - 1$ and $p = m + 1$ that is, $m = 2$, $p = 3$. Therefore $p = 3$ and $n = 1$ or $n = 3$. The answer is (C).