Solutions of the Cubic Fermat Equation in Quadratic Fields
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- title
- Solutions of the Cubic Fermat Equation in Quadratic Fields
- author
- Jones, Marvin
- 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
- 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
- type
- Thesis