Publication Date

5-2024

Date of Final Oral Examination (Defense)

March 2024

Type of Culminating Activity

Thesis

Degree Title

Master of Science in Mathematics

Department Filter

Mathematics

Department

Mathematics

Supervisory Committee Chair

Marion Scheepers, Ph.D.

Supervisory Committee Member

Liljana Babinkostova, Ph.D.

Supervisory Committee Member

Michal Kopera, Ph.D.

Abstract

The Diophantine equation x2 - Dy2 = k has been explored since antiquity and has found significant applications in diverse contexts in mathematics. This thesis focuses on two aspects of solutions of this equation:

  1. For fixed k, the sizes of the D values for which there is a solution, and the corresponding sizes of the x and y constituting solutions. This topic is previously uninvestigated and our contribution is data-based.
  2. For fixed k and D for which the equation is solvable, statistical properties of the x and y occurring in these solutions. We prove that Benford's Law applies to the solution sets.

DOI

https://doi.org/10.18122/td.2219.boisestate

Included in

Mathematics Commons

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