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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Engelhard, David R."],"institution":null,"degree_name":"Master of Science (MS) in Mathematics","degree_level":"Thesis: EWU Only","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1974,"date_issued":"1974-01-01T08:00:00Z","date_published":"1974-01-01T08:00:00Z","updated_at":"2026-07-24T02:13:07Z","subjects":["Number Theory","Other Mathematics"],"languages":[],"rights":["Access perpetually restricted to EWU users with an active EWU NetID"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.ewu.edu/theses/916","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Engelhard, David R."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis: EWU Only"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS) in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Number Theory","Other Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Access perpetually restricted to EWU users with an active EWU NetID"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://dc.ewu.edu/theses/916"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Fermat's conjecture and the factorization of F[subscript 7]"]}]}],"canonical_facts":{"dc:creator":["Engelhard, David R."],"dc:description.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.
"],"dc:identifier":["https://dc.ewu.edu/theses/916"],"dc:rights":["Access perpetually restricted to EWU users with an active EWU NetID"],"dc:subject":["Number Theory","Other Mathematics"],"dc:title":["Fermat's conjecture and the factorization of F[subscript 7]"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis: EWU Only"],"thesis:degree_name":["Master of Science (MS) in Mathematics"]},"updated_at":"2026-07-24T02:13:07Z"}