Question 41
Let $p$ be an odd prime. For every positive integer $a$, define
$$S_a=\frac a1+\frac{a^2}2+\cdots+\frac{a^{p-1}}{p-1}.$$
Let positive integers $m,n$ satisfy $S_3+S_4-3S_2=m/n$. Prove that $p$ divides $m$.
$$S_a=\frac a1+\frac{a^2}2+\cdots+\frac{a^{p-1}}{p-1}.$$
Let positive integers $m,n$ satisfy $S_3+S_4-3S_2=m/n$. Prove that $p$ divides $m$.