# 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} }

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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