Main content

A Generalization of Wilson's Theorem

Show full item record

Title: A Generalization of Wilson's Theorem
Author: Jeffery, Thomas
Department: Department of Mathematics and Statistics
Program: Mathematics and Statistics
Advisor: Pereira, Rajesh
Abstract: Wilson’s theorem states that if p is a prime number then (p−1)! ≡ −1 (mod p). One way of proving Wilson’s theorem is to note that 1 and p − 1 are the only self-invertible elements in the product (p − 1)!. The other invertible elements are paired off with their inverses leaving only the factors 1 and p−1. Wilson’s theorem is a special case of a more general result that applies to any finite abelian group G. In order to apply this general result to a finite abelian group G, we are required to know the self-invertible elements of G. In this thesis, we consider several groups formed from polynomials in quotient rings. Knowing the self-invertible elements allows us to state Wilson-like results for these groups. Knowing the order of these groups allows us to state Fermat-like results for these groups. The required number theoretical background for these results is also included.
Date: 2018-11
Rights: Attribution 4.0 International
Terms of Use: All items in the Atrium are protected by copyright with all rights reserved unless otherwise indicated.

Files in this item

Files Size Format View
Jeffery_Thomas_201812_Msc.pdf 525.5Kb PDF View/Open

This item appears in the following Collection(s)

Show full item record

Attribution 4.0 International Except where otherwise noted, this item's license is described as Attribution 4.0 International