1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook