Nontrivial solutions to the Fermat equation $x^3+y^3=k{z}^3$ over quadratic number fields

Alejandro Argaez-Garcia, Javier Diaz-Vargas, Luis Eli Pech-Moreno

We give sufficient conditions to determine the existence of nontrivial solutions to the Fermat equation $x^3+y^3=k{z}^3$ over $\mathbb{Q}(\sqrt{d})$ by constructing a relationship wi…