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

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

2006-04-19

arxiv.org/abs/math/0604425v1

Acta Arith. 125, 79-88 (2006)

Mathematics

Number Theory

10 pages

Scientific paper

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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