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!

I What is a good way to introduce Wilson's Theorem?

  1. Apr 24, 2017 #1
    What is the most motivating way to introduce Wilson’s Theorem? Why is Wilson’s theorem useful? With Fermat’s little Theorem we can say that working with residue 1 modulo prime p makes life easier but apart from working with a particular (p-1) factorial of a prime what other reasons are there for Wilson’s theorem to be useful?

    Are there any good resources on this topic?
     
  2. jcsd
  3. Apr 24, 2017 #2

    fresh_42

    Staff: Mentor

    I doubt that there is a practical use. However, it is a quite funny result, especially if formulated as
    $$
    (n-1)! \equiv \begin{cases} -1 \;(\operatorname{mod} n)& \textrm{ if } n \textrm{ prime }\\
    2 \;(\operatorname{mod} n)& \textrm{ if } n =4\\
    0 \;(\operatorname{mod} n)& \textrm{ other cases }\end{cases}
    $$
    or elegant as ##(p-1)! \equiv -1\; (\operatorname{mod} p) \Leftrightarrow p \textrm{ prime }##.

    I also find the historical part interesting as Wilson only re-discovered it 700 years later:
    https://en.wikipedia.org/wiki/Ibn_al-Haytham#Number_theory
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: What is a good way to introduce Wilson's Theorem?
Loading...