On the Number of Rational Squares at Fixed Distance from a Fifth Power

نویسنده

  • MICHAEL STOLL
چکیده

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 y = x+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 = 18 .

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تاریخ انتشار 2006