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# On the Rational Points of the Curve $f(X,Y)^q = h(X)g(X,Y)$

Published:2009-03-01
Printed: Mar 2009
• Dimitrios Poulakis
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## Abstract

Let $q = 2,3$ and $f(X,Y)$, $g(X,Y)$, $h(X)$ be polynomials with integer coefficients. In this paper we deal with the curve $f(X,Y)^q = h(X)g(X,Y)$, and we show that under some favourable conditions it is possible to determine all of its rational points.
 MSC Classifications: 11G30 - Curves of arbitrary genus or genus \$ 14G05 - Rational points 14G25 - Global ground fields