Parametric solutions to the generalized Fermat equation
In this paper we examine parametric solutions to the generalized Fermat equation, xp+yq=zr. Simple criteria are given for the existence of solutions over an algebraically closed field and all such solutions are described. Parametric solutions over non-algebraically closed fields are then considered,...
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McGill University
1999
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ndltd-LACETR-oai-collectionscanada.gc.ca-QMM.215502014-02-13T03:49:25ZParametric solutions to the generalized Fermat equationEsmonde, Jody.Mathematics.In this paper we examine parametric solutions to the generalized Fermat equation, xp+yq=zr. Simple criteria are given for the existence of solutions over an algebraically closed field and all such solutions are described. Parametric solutions over non-algebraically closed fields are then considered, along with an investigation of the number of distinct classes of solutions, up to an appropriate notion of equivalence.McGill UniversityDarmon, Henri (advisor)1999Electronic Thesis or Dissertationapplication/pdfenalephsysno: 001655328proquestno: MQ50765Theses scanned by UMI/ProQuest.All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated.Master of Science (Department of Mathematics and Statistics.) http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=21550 |
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NDLTD |
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en |
| format |
Others
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NDLTD |
| topic |
Mathematics. |
| spellingShingle |
Mathematics. Esmonde, Jody. Parametric solutions to the generalized Fermat equation |
| description |
In this paper we examine parametric solutions to the generalized Fermat equation, xp+yq=zr. Simple criteria are given for the existence of solutions over an algebraically closed field and all such solutions are described. Parametric solutions over non-algebraically closed fields are then considered, along with an investigation of the number of distinct classes of solutions, up to an appropriate notion of equivalence. |
| author2 |
Darmon, Henri (advisor) |
| author_facet |
Darmon, Henri (advisor) Esmonde, Jody. |
| author |
Esmonde, Jody. |
| author_sort |
Esmonde, Jody. |
| title |
Parametric solutions to the generalized Fermat equation |
| title_short |
Parametric solutions to the generalized Fermat equation |
| title_full |
Parametric solutions to the generalized Fermat equation |
| title_fullStr |
Parametric solutions to the generalized Fermat equation |
| title_full_unstemmed |
Parametric solutions to the generalized Fermat equation |
| title_sort |
parametric solutions to the generalized fermat equation |
| publisher |
McGill University |
| publishDate |
1999 |
| url |
http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=21550 |
| work_keys_str_mv |
AT esmondejody parametricsolutionstothegeneralizedfermatequation |
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1716639662505721856 |