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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 (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Diophantine equations -- Research, Reciprocity theorems, Modular arithmetic, Fermat's last theorem | ||||
Official Date: | October 2009 | ||||
Dates: |
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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Publication Status: | Unpublished | ||||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 |
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