Question 89
Let $n$ be a positive integer and $p \gt n + 1$ a prime. Prove that $p$ divides the following sum
$$
S = 1^{n} + 2^{n} + \ldots + (p-1)^{n}.
$$
$$
S = 1^{n} + 2^{n} + \ldots + (p-1)^{n}.
$$
MathNet 2019-part-06 — 184 problems (EN–VI) Question 89
Math Olympiad Vault · MathNet 2019-part-06 — 184 problems (EN–VI)