On the number of rational squares at fixed distance from a fifth power
Number Theory
2015-06-26 v1
Abstract
The main result of this note is that there are at most seven rational points (including the one at infinity) on the curve C_A with the affine equation y^2 = x^5 + A (where A is a tenth power free integer) when the Mordell-Weil rank of the Jacobian of C_A is one. This bound is attained for A = 18^2.
Keywords
Cite
@article{arxiv.math/0604425,
title = {On the number of rational squares at fixed distance from a fifth power},
author = {Michael Stoll},
journal= {arXiv preprint arXiv:math/0604425},
year = {2015}
}
Comments
10 pages