Nontrivial solutions to the Fermat equation x³+y³=kz³ over quadratic number fields

2023/04/14 by Argaez-Garcia, Alejandro, Diaz-Vargas, Javier, Pech-Moreno, Luis Eli
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2304.07339

Abstract

We give sufficient conditions to determine the existence of nontrivial solutions to the Fermat equation x³+y³=kz³ over ℚ(√(d)) by constructing a relationship with the points on the elliptic curve y²=x³-432d³k² over ℚ for certain k∈ℕ.

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