# Proofs of Power Sum and Binomial Coefficient Congruences Via Pascal's Identity

```@article{MacMillan2011ProofsOP,
title={Proofs of Power Sum and Binomial Coefficient Congruences Via Pascal's Identity},
author={Kieren MacMillan and Jonathan Sondow},
journal={The American Mathematical Monthly},
year={2011},
volume={118},
pages={549 - 551}
}```
• Published 30 October 2010
• Mathematics
• The American Mathematical Monthly
Abstract A well-known and frequently cited congruence for power sums is where n ≥ 1 and p 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 Pascal in 1654. An application is a simple proof of a congruence for certain sums of binomial coefficients, due to Hermite and Bachmann.
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