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Re: Wilson's theorem and divisibilty properties of n!+-1, n!^2+1, etc

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  • ajw01@uow.edu.au
    ... been ... Actually, Flavio Torasso has pointed out that in the preprint available at http://www.utm.edu/~caldwell/preprints/primorials.pdf. there is a
    Message 1 of 3 , May 29, 2001
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      --- In primenumbers@y..., ajw01@u... wrote:
      > --- In primenumbers@y..., ajw01@u... wrote:
      > >
      > > I've been looking at Chris Caldwell and Yves Gallot's paper on
      > > the primality of n!+-1 and 2*3*5*...*p+-1 which is in the list of
      > > recently submitted papers for Mathematics of Computation. In it
      > > are a number of interesting divisibility properties which have
      been
      > > known for a while but are good to see in one place. To summarise
      > > they are, as given in the paper:
      > >
      > > ii) If n is prime, then n divides both (n-1)!+1 and (n-2)!-1
      > > iii) If n is odd and 2n+1 is prime, then 2n+1 divides exactly one
      > > of n!+-1
      > > iv) If the prime p divides n!+-1, then p-n-1 divides one of n!+-1
      > >
      Actually, Flavio Torasso has pointed out that in the preprint
      available at http://www.utm.edu/~caldwell/preprints/primorials.pdf.
      there is a mistake, iv) as prooved does not match the iv) above
      which I copied from the preprint. It should in fact read
      iv) If the prime p divides n!+-1 then p divides exactly one of
      (p-n-1)!+1

      Andrew Walker
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