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

  title={Proofs of Power Sum and Binomial Coefficient Congruences Via Pascal's Identity},
  author={Kieren MacMillan and Jonathan Sondow},
  journal={The American Mathematical Monthly},
  pages={549 - 551}
  • Kieren MacMillan, Jonathan Sondow
  • Published 2011
  • Mathematics, Computer Science
  • 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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