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arXiv · 2304.07339

Nontrivial solutions to the Fermat equation $x^3+y^3=kz^3$ over quadratic number fields

Alejandro Argaez-Garcia·Javier Diaz-Vargas·Luis Eli Pech-Moreno
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Abstract

We give sufficient conditions to determine the existence of nontrivial solutions to the Fermat equation $x^3+y^3=kz^3$ over $\mathbb{Q}(\sqrt{d})$ by constructing a relationship with the points on the elliptic curve $y^2=x^3-432d^3k^2$ over $\mathbb{Q}$ for certain $k\in\mathbb{N}$.

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Alejandro Argaez-Garcia, Javier Diaz-Vargas, Luis Eli Pech-Moreno. 2025-01-17. Nontrivial solutions to the Fermat equation $x^3+y^3=kz^3$ over quadratic number fields. https://doi.org/10.17654/0972555525018

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