{"id":{"repo_id":"brock","oai_identifier":"oai:brocku.scholaris.ca:10464/18168"},"canonical_url":"https://search.dev.ndltd.org/etd/brock/oai:brocku.scholaris.ca:10464/18168","repository":{"repo_id":"brock","name":"Brock University","base_url":"https://brocku.scholaris.ca/server/oai/request"},"display":{"title":"On the Extendibility of a D(4)-Pair of Pell Numbers","abstract":"A 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.","abstract_html":"A 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.","abstract_has_math":false,"creators":["Emanuel, David"],"institution":"Brock University","degree_name":"M.Sc. Mathematics and Statistics","degree_level":"Masters","degree_discipline":"Faculty of Mathematics and Science","degree_department":"Department of Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-10-16T17:24:02Z","date_published":"2023-10-16T17:24:02Z","updated_at":"2026-07-24T01:23:00Z","subjects":["Linear forms in logarithms","Diophantine triples","Pell's equation","Pell numbers"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10464/18168","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Department of Mathematics"]},{"key":"dc:creator","label":"Author","values":["Emanuel, David"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2023-10-16T17:24:02Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2023-10-16T17:24:02Z"]},{"key":"dc:date.issued","label":"Date","values":["2023-10-16T17:24:02Z"]},{"key":"dc:type","label":"Dc Type","values":["Electronic Thesis or Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Faculty of Mathematics and Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.Sc. 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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."]},{"key":"dc:title","label":"Title","values":["On the Extendibility of a D(4)-Pair of Pell Numbers"]}]}],"canonical_facts":{"dc:contributor.department":["Department of Mathematics"],"dc:creator":["Emanuel, David"],"dc:date.accessioned":["2023-10-16T17:24:02Z"],"dc:date.available":["2023-10-16T17:24:02Z"],"dc:date.issued":["2023-10-16T17:24:02Z"],"dc:description.abstract":["A 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."],"dc:identifier.uri":["http://hdl.handle.net/10464/18168"],"dc:language.iso":["eng"],"dc:subject":["Linear forms in logarithms","Diophantine triples","Pell's equation","Pell numbers"],"dc:title":["On the Extendibility of a D(4)-Pair of Pell Numbers"],"dc:type":["Electronic Thesis or Dissertation"],"thesis:degree_discipline":["Faculty of Mathematics and Science"],"thesis:degree_level":["Masters"],"thesis:degree_name":["M.Sc. Mathematics and Statistics"],"thesis:institution_name":["Brock University"]},"updated_at":"2026-07-24T01:23:00Z"}