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arXiv · 1211.3610

Solutions of the cubic Fermat equation in quadratic fields

Marvin Jones·Jeremy Rouse
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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.

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Marvin Jones, Jeremy Rouse. 2012-11-15. Solutions of the cubic Fermat equation in quadratic fields. https://doi.org/10.1142/s1793042113500449

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