On Modular Approach to Diophantine Equation $x^4-y^4=nz^p$ over Number Fields
Number Theory
2023-11-22 v1
Abstract
Recent results of Freitas, Kraus, Sengun and Siksek give sufficient criteria for the asymptotic Fermat's Last Theorem to hold over various number fields. In this paper, we prove asymptotic results about the solutions of the Diophantine equation over various number fields using the modular method. For instance, we prove that the asymptotic generalised Fermat Theorem for the equation holds for infinitely many quadratic number fields.
Keywords
Cite
@article{arxiv.2311.12044,
title = {On Modular Approach to Diophantine Equation $x^4-y^4=nz^p$ over Number Fields},
author = {Erman Isik},
journal= {arXiv preprint arXiv:2311.12044},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:2201.13270