Abstract
dc:description.abstractA Diophantine m-tuple with property D(ℓ) is a set of m integers such that the product of any two integers plus ℓ results in a perfect square. This thesis establishes that a particular family of D(4) pairs of Pell numbers can be extended to a D(4) triple by exactly one Pell number. A similar result has been found for the Diophantine triples of Fibonacci numbers, a discussion of which is included in the first chapter of this thesis. This chapter finishes with a statement of the main result of my thesis, and the subsequent chapters discuss several topics in number theory which were used to prove the main result in chapter 5. Specifically, results about continued fractions, Pell-type equations, and linear forms in logarithms were used. These topics are the subjects of chapters 2, 3 and 4, which contain some history and discussions of the important results. The conclusion of this thesis discusses some possible generalizations.
Degree
thesis:*- Name thesis:degree_name
- M.Sc. Mathematics and Statistics
- Level thesis:degree_level
- Masters
- Discipline thesis:degree_discipline
- Faculty of Mathematics and Science
- Department dc:contributor.department
- Department of Mathematics
- Grantor
- Brock University
- Year dc:date.issued
- 2023
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Emanuel, David
Subjects
dc:subject × 4Rights
- Language dc:language.iso
- eng
Identifiers
dc:identifier.*- Handle dc:identifier.uri
- http://hdl.handle.net/10464/18168
- OAI identifier oai:identifier
- oai:brocku.scholaris.ca:10464/18168