Question: Prove that n 5 - n is divisible by 5 for any n N. use either a proof of induction on n or the division

  1. Prove that n5 - n is divisible by 5 for any n N. use either a proof of induction on n or the division algorithm on n and a proof by cases. (choose which method you prefer).

Identities that may be helpful depending on your chosen proof technique:

  • (n + 1)5 = n5 + 5n4 + 10n3 + 10n2 + 5n + 1
  • n5 - n = n(n2 + 1)(n + 1)(n1)

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