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Wilson corollary

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  • Jon Perry
    Consider the sequence of integers p+1,...p+k, p a prime. The product of these integers is k! mod p. Let k=p-1, therefore k! mod p = (p-1)! mod p = -1 mod p.
    Message 1 of 1 , Jun 24, 2002
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      Consider the sequence of integers p+1,...p+k, p a prime.

      The product of these integers is k! mod p.

      Let k=p-1, therefore k! mod p = (p-1)! mod p = -1 mod p.

      Therefore (p+1)...(2p-1) = -1 mod p

      e.g. 8.9.10.11.12.13 = 1235520 = 176503*7-1 = -1mod7

      Jon Perry
      perry@...
      http://www.users.globalnet.co.uk/~perry/maths
      BrainBench MVP for HTML and JavaScript
      http://www.brainbench.com
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