Master's Thesis Defense

April 30th at 4pm in Manchester 020

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 there to be non-trivial solutions for certain values of $d$ squarefree but not all. Our argument assumes the Birch-Swinnerton-Dyer conjecture and follows a similar argument as Tunnell's solution to the congruent number problem.