Perfect powers expressible as sums of two fifth or seventh powers
Number Theory
2014-01-28 v2
Abstract
We show that the generalized Fermat equations with signatures (5,5,7), (5,5,19), and (7,7,5) (and unit coefficients) have no non-trivial primitive integer solutions. Assuming GRH, we also prove the nonexistence of non-trivial primitive integer solutions for the signatures (5,5,11), (5,5,13), and (7,7,11). The main ingredients for obtaining our results are descent techniques, the method of Chabauty-Coleman, and the modular approach to Diophantine equations.
Keywords
Cite
@article{arxiv.1309.4030,
title = {Perfect powers expressible as sums of two fifth or seventh powers},
author = {Sander R. Dahmen and Samir Siksek},
journal= {arXiv preprint arXiv:1309.4030},
year = {2014}
}
Comments
The current version incorporates minor comments of the referee