Question 28
Denote $S_a = \frac{a}{1} + \frac{a^2}{2} + \dots + \frac{a^{p-1}}{p-1}$ for any whole number $a$. Prove that if for any whole number $n$ the relation $S_{2n} + S_{2n-1} - 2S_n - S_2 = \frac{m}{k}$, (where $m, k$ are relatively prime) holds then $m$ is divisible by $p$.