Summary: A well-known and frequently cited congruence for power sums is
where and is prime. We survey the main ingredients in several known proofs. Then we give an elementary proof, using an identity for power sums proven by B. Pascal in the year 1654. An application is a simple proof of a congruence for certain sums of binomial coefficients, due to Ch. Hermite [J. Reine Angew. Math. 81, 93–95 (1875; JFM 07.0131.01)] and P. Bachmann [Niedere Zahlentheorie. Zweiter Teil, Teubner, Leipzig (1910; JFM 41.0221.10) (p. 53); Reprint. Bronx, N. Y.: Chelsea (1968; Zbl 0253.10001)].