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

14340Re: Wilson's sexy twin cousin? and new function?

Expand Messages
  • richard_heylen
    Jan 7, 2004
      --- In primenumbers@yahoogroups.com, "John W. Nicholson"
      <johnw.nicholson@s...> wrote:
      > I am reading The Little Book of Big Primes by Paulo Ribenboim. I'm
      > on page 145 trying to figure out the steps for proving:
      > (== means congruent)
      >
      > 4((n-1)!+1)+n == 0 (mod n(n+2))
      >
      > the first step is stating Wilson's theorem as the following:
      >
      > (n-1)!+1 == 0 (mod n) which is has been proved earlier in the book.
      >
      > the next thing is one of the places where I am getting lost:
      >
      > 4(n-1)!+2 == 0 (mod (n+2))
      >
      > It seems like this statement was pulled out of the blue. Where did
      > it come from?

      It's a sloppy change of variables. Set m+2=n then
      (m+2-1)! +1 == 0 (mod m+2)
      (m+1)(m)(m-1)!+1 == 0 (mod m+2)
      (-1)(-2)(m-1)!+1 == 0 (mod m+2)
      2(m-1)!+1 == 0 (mod m+2)
      QED

      Rick
    • Show all 2 messages in this topic