#### Date on Master's Thesis/Doctoral Dissertation

5-1940

#### Document Type

Master's Thesis

#### Degree Name

M.A.

#### Department

Mathematics

#### Degree Program

Mathematics, MA

#### Committee Chair

Loewner, Charles

#### Committee Co-Chair (if applicable)

Stevenson, Guy

#### Committee Member

Moore, Walter L.

#### Subject

Fermat's last theorem

#### Abstract

This work is intended primarily for the student of mathematics who may not necessarily wish to delve into the complete theory of the problem. but who may wish to get a picture of the work necessary to study and understand it. For a complete history of the problem until 1919, refer to Chapter XXVI of Dickson's History of the Theory of Numbers, II, and for the work primarily connected with Irregular Cyclotomic Fields and Fermat's Last Theorem through part of 1927, refer to Algebraic Numbers, II, National Research Council Bulletin, # 62. For a Short presentation of the problem refer to Mordell, Three Lectures on Fermat's Last Theorem. For a more detailed analysis of the methods used to work on this problem refer to Bachmann, Das Fermatproblem. The author of this treatise has attempted to cover certain points. First, to give the nature of Fermat's Last Theorem. Second, an introduction. which will contain some historical facts of the Last Theorem, a reference to the mathematical development which resulted from this problem and its status at the present. Third, a detailed account of the method of infinite descent. The cases n = 3, 4. 5 are used to show this method of attack. For n = 5 the procedure is that of Dirichlet. In order that a better understanding may be secured of various steps in his proof. all the theorems of his article are reproduced without proof. Fourth. an introduction to the theory of ideals. This is not an exhaustive study of ideals but an attempt to aid the beginner to understand them.

#### Recommended Citation

Krumpelman, Jerome L., "A study of Fermat's last theorem." (1940). *Electronic Theses and Dissertations.* Paper 1993.

http://dx.doi.org/10.18297/etd/1993