Solutions of the cubic Fermat equation in quadratic fields

Abstract

We give necessary and sufficient conditions on a squarefree integer $d$ for there to be non-trivial solutions to $x^3+y^3=z^3$ in $\Q(\sqrt{d})$, conditional on the Birch and Swinnerton-Dyer conjecture. These conditions are similar to those obtained by J. Tunnell in his solution to the congruent number problem.

12 pages

Cited by in corpus (1)

• Solutions of the cubic Fermat equation in ring class fields of imaginary quadratic fields (as periodic points of a 3-adic algebraic function)