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Modular and reciprocity approaches to a family of diophantine equations
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Ibrahim, Mostafa (2009) Modular and reciprocity approaches to a family of diophantine equations. PhD thesis, University of Warwick.
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Abstract
In this thesis we study the Diophantine equation xp - Dy2p = z2; gcd(x; z) = 1; p prime: We combine two approaches: - The modular approach using in Wiles's proof of Fermat's Last Theorem. - Elementary quadratic reciprocity. We show how using this combination of approaches and computer calculations we can get congruence conditions for the exponent p.
| Item Type: | Thesis or Dissertation (PhD) |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Library of Congress Subject Headings (LCSH): | Diophantine equations -- Research, Reciprocity theorems, Modular arithmetic, Fermat's last theorem |
| Date: | October 2009 |
| Institution: | University of Warwick |
| Theses Department: | Mathematics Institute |
| Thesis Type: | PhD |
| Publication Status: | Unpublished |
| Supervisor(s)/Advisor: | Siksek, Samir |
| Sponsors: | Engineering and Physical Sciences Research Council (Great Britain) (EPSRC) |
| Format of File: | |
| Extent: | 140 leaves : charts |
| Language: | eng |
| URI: | http://wrap.warwick.ac.uk/id/eprint/2761 |
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