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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] = 2²[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/F₅ and therefore, F₅ is composite. In this thesis I will use Lucas' and Euler's criterion to develop a method which will factor certain composite F₈. Of special interest n will be F₇ and F₈, F₇ because it was only recently factored and F₈ because it never has been factored. I will show this method works for F₇ and give conditions for the factorization of F₈.
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Recommended Citation
Engelhard, David R., "Fermat's conjecture and the factorization of F[subscript 7]" (1974). EWU Masters Thesis Collection. 916.
https://dc.ewu.edu/theses/916
