On the number of rational squares at fixed distance from a fifth power
arXiv:math/0604425 · doi:10.4064/aa125-1-7
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.
10 pages