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Wilson theorem Question Explanation

  1. Nov 3, 2008 #1
    How do I explain this:

    Let [tex]p[/tex] be odd prime explain why: [tex]2*4*...*(p-1)\equiv (2-p)(4-p)*...*(p-1-p)\equiv(-1)^{\frac{(p-1)}{2}}*1*3*...*(p-2)[/tex] mod [tex]p[/tex].

    Relevant equations

    Gauss lemma
    wilson's theorem [[tex](p-1)!\equiv-1[/tex] mod[tex] p[/tex]]

    The attempt at a solution
    pairing? need assistance

  2. jcsd
  3. Nov 3, 2008 #2


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    Homework Helper
    Gold Member

    Hint: What are [itex]2-(2-p)[/itex], [itex]4-(4-p)[/itex], ... [itex](p-1)-(p-1-p)[/itex]? Are they divisible by [itex]p[/itex]?
  4. Nov 3, 2008 #3
    Thanks, this problem is solved.
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