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Solutions of the Cubic Fermat Equation in Quadratic Fields

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abstract
We will examine when there are nontrivial solutions to the equation $x^3 + y^3 = z^3$ in $\mathbb{Q}(\sqrt{d})$ for a squarefree integer $d$. In this variation of Fermat's Last Theorem, it is possible for nontrivial solutions to exist in $\mathbb{Q}(\sqrt{d})$ for some choices of $d$, but not for all. Our argument assumes the Birch and Swinnerton-Dyer conjecture and follows a similar argument as Tunnell's solution to the congruent number problem.
subject
elliptic curves
fermat's last theorem
modular forms
quadratic fields
contributor
Jones, Marvin (author)
Rouse, Jeremy A (committee chair)
Howard, Fredric T (committee member)
Berenhaut, Kenneth S (committee member)
date
2012-06-12T08:35:51Z (accessioned)
2012-06-12T08:35:51Z (available)
2012 (issued)
degree
Mathematics (discipline)
identifier
http://hdl.handle.net/10339/37265 (uri)
language
en (iso)
publisher
Wake Forest University
title
Solutions of the Cubic Fermat Equation in Quadratic Fields
type
Thesis

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