# On the number of rational squares at fixed distance from a fifth power

@article{Stoll2006OnTN, title={On the number of rational squares at fixed distance from a fifth power}, author={Michael Stoll}, journal={Acta Arithmetica}, year={2006}, volume={125}, pages={79-88} }

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.

#### 7 Citations

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In this paper, we study bounds for the number of rational points on twists $C'$ of a fixed curve $C$ over a number field ${\mathcal K}$, under the condition that the group of ${\mathcal K}$-rational… Expand

E-mail address: m.stoll@iu-bremen

- E-mail address: m.stoll@iu-bremen