On the number of rational squares at fixed distance from a fifth power
Michael Stoll
Abstract
The main result of this note is that there are at most seven rational points (including the one at infinity) on the curve CA with the affine equation y2 = x5 + A (where A is a tenth power free integer) when the Mordell-Weil rank of the Jacobian of CA is one. This bound is attained for A = 182.
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