What constitutes an adequate solution to a mathematical problem? When is an adequate solution a 'good' solution? In this thesis I consider these questions in relation to two Diophantine equations, namely, x$ sp2$ + k = y$ sp3$ and 6y$ sp2$ = x(x + 1)(2x + 1). The first dates back to Diophantus himself (c. 250 AD) while the second can be traced to a puzzle proposed by Edouard Lucas in 1875. Each of these equations has attracted a number of solutions and each solution reveals something about its era. An examination and comparison of these solutions will give us an opportunity to reflect on some of the criteria used for judging proofs in mathematics. In particular, we shall see that contemporary computer technology has made a certain kind of solution to these equations acceptable which might have seemed pointless, incomplete or inelegant to the mathematicians who first studied them. Included among these 'computer solutions' is my own solution to 6y$ sp2$ = x(x + 1)(2x + 1).
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.72100 |
| Date | January 1987 |
| Creators | Anglin, William Sherron Raymond. |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Mathematics and Statistics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 000417611, proquestno: AAINL44377, Theses scanned by UMI/ProQuest. |
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