Modular and reciprocity approaches to a family of diophantine equations
Ibrahim, Mostafa (2009) Modular and reciprocity approaches to a family of diophantine equations. PhD thesis, University of Warwick.
WRAP_THESIS_Ibrahim_2009.pdf - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
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|
|Official Date:||October 2009|
|Institution:||University of Warwick|
|Theses Department:||Mathematics Institute|
|Sponsors:||Engineering and Physical Sciences Research Council (Great Britain) (EPSRC)|
|Format of File:|
|Extent:||140 leaves : charts|
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