Question 12
Let $p \gt 3$ be a prime number. Yes
$$
\frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \dots + \frac{1}{(p-1)^2} = \frac{n}{m}
$$
where the greatest common divisor of $n$ and $m$ is $1$, show that $p^3$ divides $n$.
$$
\frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \dots + \frac{1}{(p-1)^2} = \frac{n}{m}
$$
where the greatest common divisor of $n$ and $m$ is $1$, show that $p^3$ divides $n$.