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18569Re: Factorial flight of fancy

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  • thefatphil
    Jan 16, 2007
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      --- In primenumbers@yahoogroups.com, Phil Carmody <thefatphil@...>
      wrote:

      [Stuff - just see: http://tech.groups.yahoo.com/group/primenumbers/
      message/18206?threaded=1&var=1&l=1 ]

      On sci.math just now, Gerry Myerson has chipped in the following:

      <<<
      It's shown in Niven, Zuckerman, and Montgomery that if p is 1 mod 4
      then ( (p - 1) / 2 ) factorial squared is -1 mod p (p. 54), and
      it's an exercise to show that if p is 3 mod 4 then the quantity is
      plus-or-minus 1 (exercise 2.1.18).

      Maybe something interesting happens with ( (p - 1) / 3 ) factorial,
      for those primes congruent 1 mod 3.
      >>>

      I instantaniously bought Niven, Zuckerman, and Montgomery (huge, not
      petit), and unless anyone else wants to chip in with a review right
      now, I shall do so when it arrives in a month or so.

      G^HMerry unorthodox Christmas to me!

      Phil
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