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Re: A nice problem...

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  • Werner D. Sand
    ... (p-1) ... is ... This is not a property of the prime numbers but of the natural numbers: put n instead of p, or, if you want, 2n-1 (odd numbers). WDS
    Message 1 of 3 , Dec 31, 2007
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      --- In primenumbers@yahoogroups.com, "S. R. Sudarshan Iyengar"
      <sudarshanmysore@...> wrote:
      >
      > Here goes a nice problem... IT would be nice if someone can give me
      > links/references where I can find more details about this problem.
      >
      > Given a prime P its easy to see that it always divides 1+ 2 + .. +
      (p-1)
      >
      > But it in fact divides 1^k + 2^k + ... + (p-1)^k for all k except 0
      > and p-1.
      >
      > Its obvious if k is odd. But is there any way of proving it when k
      is
      > even?
      >
      > Regards,
      > Sudarshan
      >


      This is not a property of the prime numbers but of the natural
      numbers: put n instead of p, or, if you want, 2n-1 (odd numbers).

      WDS
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