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Modular and reciprocity approaches to a family of diophantine equations

By Mostafa Ibrahim

Abstract

In this thesis we study the Diophantine equation\ud xp - Dy2p = z2; gcd(x; z) = 1; p prime:\ud We combine two approaches:\ud - The modular approach using in Wiles's proof of Fermat's Last Theorem.\ud - Elementary quadratic reciprocity.\ud We show how using this combination of approaches and computer calculations we can get congruence conditions for the exponent p

Topics: QA
OAI identifier: oai:wrap.warwick.ac.uk:2761

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