Loading ...
Sorry, an error occurred while loading the content.

Re: [PrimeNumbers] Wolstenholme's Theorem

Expand Messages
  • Phil Carmody
    ... Many thanks Ignacio! The formulation of the theorem I have seen was different, but closely related (namely the C(2p-1,p-1) one), and hopefully not too much
    Message 1 of 3 , Sep 4, 2006
    • 0 Attachment
      --- Ignacio Larrosa CaƱestro <ilarrosa@...> wrote:
      > Monday, September 04, 2006 6:21 PM [GMT+1=CET],
      > Phil Carmody <thefatphil@...> escribiĆ³:
      > > I don't suppose anyone can sketch a proof of it, could they?
      >
      > I think there are two or more versions of the theorem, related I suppose. In
      > "Introduction to Analytic Number Theory" of T. M. Apostol, there is this:
      >
      > If p >= 5 is prime, then
      >
      > S_{p-2} = Sum((p - 1)!/k, k, 1, p-1) = 0 (mod p^2)
      ...
      > ===> S_{p-2} = 0 (mod p^2) (q.e.d.)

      Many thanks Ignacio! The formulation of the theorem I have seen was different,
      but closely related (namely the C(2p-1,p-1) one), and hopefully not too much of
      a leap from the above.

      In particular, I think I noticed that on Dave Rusin's archive of useful
      sci.math.* posts, there's a discussion which seems to relate the two
      formulations.

      I thought I spotted a generalisation (of the other formulation), and wished to
      prove it before relying on its truth!

      Thanks again,
      Phil

      () ASCII ribbon campaign () Hopeless ribbon campaign
      /\ against HTML mail /\ against gratuitous bloodshed

      [stolen with permission from Daniel B. Cristofani]

      __________________________________________________
      Do You Yahoo!?
      Tired of spam? Yahoo! Mail has the best spam protection around
      http://mail.yahoo.com
    Your message has been successfully submitted and would be delivered to recipients shortly.