MathNet 2014 Question 14

Let $p \geq 2$ be a prime number and $\frac{a_{p}}{b_{p}} = 1 + \frac{1}{2} + \cdots + \frac{1}{p^{2}-1}$, where $a_{p}$ and $b_{p}$ are two relatively prime positive integers. Compute $\operatorname{gcd}\left(p, b_{p}\right)$.