1. Not finding help here? Sign up for a free 30min 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!

Abstract help

  1. Dec 7, 2009 #1
    1. The problem statement, all variables and given/known data

    let p be prime then, (p-1)! is congruent to -1 mod p

    2. Relevant equations



    3. The attempt at a solution

    I'm not sure where to start
     
  2. jcsd
  3. Dec 7, 2009 #2
    First of all you should try some examples out for small prime.

    Since p is prime, the set {1, 2, ... p-1} is a group under multiplication, modulo p. This means that there is a (unique) inverse for each element.
     
  4. Dec 7, 2009 #3
    I've tried small numbers and it works. So since it has an inverse it means that it can be mod p ? I'm sorry I don't understand this stuff very well.
     
  5. Dec 8, 2009 #4
    The fact there there is an inverse means that for each element x, there is an element y such that xy = 1 mod p - and this is only true because p is a prime (a well known group theory result). The main idea for the proof of this theorem is to try to pair up each element with it's inverse (which is valid since this group is commutative).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Abstract help
  1. Abstract help! (Replies: 11)

  2. Abstract Algebra help! (Replies: 11)

  3. Abstract algebra help (Replies: 1)

Loading...