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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.

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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}
}

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10 pages