Solutions of the cubic Fermat equation in quadratic fields
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.
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