dc.contributor.author Schedler, Zak dc.date.accessioned 2019-04-08T18:26:38Z dc.date.available 2019-04-08T18:26:38Z dc.identifier.uri http://hdl.handle.net/10464/14041 dc.description.abstract A Diophantine equation is an equation of more than one variable where we are en_US looking for strictly integer solutions. The purpose of this paper is to give a new upper bounds for the number of positive solutions for the Diophantine equation $y^2 = px(Ax^2 − C), C \in {2, ±1, ±4}. Where p is an odd prime and A is an integer greater than 1. The case where C = −2 is already complete, which we go over in detail here. We look through examples of Diophantine equations starting with linear Diophantine equations. We then look at Pell’s equation,$x^2 − Dy^2 = C$where D and C are natural numbers. We show the continued fraction algorithm and how to use it to solve Pell’s equation. We will look at proofs and lemmas surrounding particular cases of the Diophantine equation$y^2 = px(Ax^2 − C)$. Then focus on finding the upper bounds of the equation. Then we conclude by showing the new upper bounds of the Diophantine equation$y^2 = px(Ax^2 − C), C \in {2, ±1, ±4}. dc.language.iso eng en_US dc.publisher Brock University en_US dc.subject Diophantine Equation en_US dc.title Upper Bounds for the Number of solutions for the Diophantine Equation $y^2=px(Ax^2-C), C \in {2, \pm 1, \pm 4}$ en_US dc.type Electronic Thesis or Dissertation en dc.degree.name M.Sc. Mathematics and Statistics en_US dc.degree.level Masters en_US dc.contributor.department Department of Mathematics en_US dc.degree.discipline Faculty of Mathematics and Science en_US refterms.dateFOA 2021-08-14T01:44:30Z
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