The Generalised Fermat Equation x^2 + y^3 = z^15
Number Theory
2016-08-03 v2
Abstract
We determine the set of primitive integral solutions to the generalised Fermat equation x^2 + y^3 = z^15. As expected, the only solutions are the trivial ones with xyz = 0 and the non-trivial pair (x,y,z) = (+-3, -2, 1).
Keywords
Cite
@article{arxiv.1309.4421,
title = {The Generalised Fermat Equation x^2 + y^3 = z^15},
author = {Samir Siksek and Michael Stoll},
journal= {arXiv preprint arXiv:1309.4421},
year = {2016}
}
Comments
The paper is slightly shorter. Specifically, in the notation of the paper, we are now able to carry out Chabauty on the curve C_{3,0}. This allows us to eliminate a lengthy elliptic curve Chabauty computation