Congruences of Power Sums

Nicholas J. Newsome, Maria S. Nogin, Adnan H. Sabuwala

The following congruence for power sums, $S_n(p)$, is well known and has many applications: $1^n+2^n +\dots +p^n \equiv\begin{cases} -1 \text{ mod } p, & \text{ if } \ p-1 \ | \ n;…