Solutions of the Cubic Fermat Equation in Quadratic Fields

We will examine when there are nontrivial solutions to the equation x³ + y³ = z³ 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.

Grantor dc:publisher

Wake Forest University

Year dc:date.issued

2012

Author dc:creator

• Jones, Marvin

• elliptic curves

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10339/37265

OAI identifier oai:identifier

oai:wakespace.lib.wfu.edu:10339/37265