Fermat's conjecture and the factorization of F[subscript 7]

<p>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.</p>

Name thesis:degree_name

Master of Science (MS) in Mathematics

Level thesis:degree_level

Thesis: EWU Only

Discipline thesis:degree_discipline

Mathematics

Year

1974

Author dc:creator

• Engelhard, David R.

• Number Theory
• Other Mathematics

Statement dc:rights

• Access perpetually restricted to EWU users with an active EWU NetID

Repository record dc:identifier

https://dc.ewu.edu/theses/916

OAI identifier oai:identifier

oai:dc.ewu.edu:theses-1916