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:
- 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.
- 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
Recommended Citation
Patterson, Christine, "The Brahmagupta Equation and Record Numbers" (2024). Boise State University Theses and Dissertations. 2219.
https://doi.org/10.18122/td.2219.boisestate