The Fermat-type equations x^5 + y^5 = 2z^p or 3z^p solved through Q-curves
Number Theory
2011-03-29 v1
Abstract
We solve the Diophantine equations with for a set of prime numbers of density 1/4, 1/2, respectively. The method consists in relating a possible solution to another Diophantine equation and solving the later by using Q-curves and a generalized modular technique as in work of Ellenberg and Dieulefait-Jimenez along with some new techniques for eliminating newforms.
Keywords
Cite
@article{arxiv.1103.5388,
title = {The Fermat-type equations x^5 + y^5 = 2z^p or 3z^p solved through Q-curves},
author = {Luis Dieulefait and Nuno Freitas},
journal= {arXiv preprint arXiv:1103.5388},
year = {2011}
}