12.2.38 Number theory

Problem: Let \( p \) is prime, greater than 3 and \( m \) and \( n \) are such coprime integers that \[ \frac{m}{n}=\frac{1}{1^{2}}+\frac{1}{2^{2}}+\cdots+\frac{1}{(p-1)^{2}} . \] Let's prove that \( m \) is divided by \( p \).