Off-campus Eastern Washington University users: To download EWU Only theses, please use the following link to log into our proxy server with your EWU NetID and password.
Non-EWU users: Please talk to your local librarian about requesting this thesis through Interlibrary loan.
Date of Award
Summer 1974
Rights
Access perpetually restricted to EWU users with an active EWU NetID
Document Type
Thesis: EWU Only
Degree Name
Master of Science (MS) in Mathematics
Department
Mathematics
Abstract
In 1640, Pierre de Fermat conjectured that numbers of the form F[subscript n] = 2 [superscript 2][superscript n]+1 are prime for. all n = 0, 1, . 2, 3, . . It is easy to establish the .validity of . this conjecture for n < 5. Fermat's idea was generally accepted as true until 1732 when Leonhard Euler dis.proved the conjecture by counter example i.e. Euler showed 641[F[subscipt 5] and therefore, F[subscript 5] is composite. In this thesis I will use Lucas' and Euler's criterion to develop a method which will factor certain composite F[subscript 8]. Of special interest n will be F[subscript 7] and F[subscript 8], F[subscript 7] because it was only recently factored and Fa because it never has been factored. I will show this method works for F[subscript 7] and give conditions for the factorization of F[subscipt 8].
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Recommended Citation
Englehard, David R., "Fermat's conjecture and the factorization of F[subscript 7]" (1974). EWU Masters Thesis Collection. 916.
https://dc.ewu.edu/theses/916
