Document Type
Thesis
Date of Degree Completion
Spring 2012
Degree Name
Bachelor of Science
Department
Mathematics
Committee Chair
Dr. Dominic Klyve, Dept. of Mathematics
Second Committee Member
Dr. James Harper, Dept. Of Mathematics
Third Committee Member
Dr. Mathew C. Altman, Dept. of Philosophy
Abstract
We examine the mathematical and historical context of Leonhard Euler's first paper on Diophantine Equations, "De Solutione Problematum Diophanteorum Per Numeros Integros," (E29). We reexamine and verify Euler's calculations, and we translate his work into modern notation. Euler struggled in working with Diophantine Equations at first, which makes his work difficult to follow. We found several perviously-unreported errors in the paper. We show how these errors can be fixed without changing the main idea of Euler's argument. We also compare E29 to another paper on Diophantine Equations which Euler wrote later in life. In this paper, Euler's mathematical ideas are much easier to understand and to verify, and his work is more complete, demonstrating that he had progressed in his understanding of this type of problem. In order to put the paper in context, other problems in Diophantine Equations such as solutions to the Pell Equation and Fermat's Last Theorem are traced back to their roots and followed to their completion, and Euler's life is examined briefly.
Recommended Citation
Livingston, Benjamin, "Euler's Early Work in Diophantine Analysis" (2012). Undergraduate Honors Theses. 85.
https://digitalcommons.cwu.edu/undergrad_hontheses/85
Comments
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