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}
}
  • M. Stoll
  • Published 2006
  • Mathematics
  • Acta Arithmetica
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. 
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Independence of rational points on twists of a given curve
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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 ${\mathcal K}$-rationalExpand
E-mail address: m.stoll@iu-bremen
  • E-mail address: m.stoll@iu-bremen