Results 1 to 2 of 2

Thread: Stuck on a congruency problem

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    5

    Stuck on a congruency problem

    I'm using Wilson's Theorem to find the remainder of 24! when divided by 29. Here are my steps thus far:

    24!*25*26*27*28 ≡ -1 mod 29

    24!*(-4)*(-3)*(-2)*(-1) ≡ -1 mod 29

    24!*24 ≡ -1 mod 29

    How do I finish off the congruency to find the remainder?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    10
    Quote Originally Posted by F350 View Post
    I'm using Wilson's Theorem to find the remainder of 24! when divided by 29. Here are my steps thus far:

    24!*25*26*27*28 ≡ -1 mod 29

    24!*(-4)*(-3)*(-2)*(-1) ≡ -1 mod 29

    24!*24 ≡ -1 mod 29

    How do I finish off the congruency to find the remainder?
    That's a good start. In fact, you're nearly there. Next step is to say that 24 ≡ 5 (mod 29), so 24!*5 ≡ 1 (mod 29). Finally 5*6 = 30 ≡ 1 (mod 29), so multiply both sides by 6 and you finish with 24! ≡ 6 (mod 29).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need help with this congruency problem
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: Dec 13th 2009, 03:03 PM
  2. Help with congruency
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: Oct 20th 2009, 02:41 AM
  3. Congruency
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: Mar 7th 2009, 01:14 PM
  4. Need help with CONGRUENCY!!! @__@?
    Posted in the Geometry Forum
    Replies: 2
    Last Post: Nov 29th 2007, 11:59 PM
  5. Congruency
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: Mar 15th 2007, 08:35 PM

Search Tags


/mathhelpforum @mathhelpforum