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

Published online by Cambridge University Press:  20 November 2018

Dimitrios Poulakis
Dimitrios Poulakis*
Affiliation:
Aristotle University of Thessaloniki, Department of Mathematics, 54124 Thessaloniki, Greece e-mail: [email protected]
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Abstract

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Let $\text{q}\,\text{=}\,\text{2,}\,\text{3}$ and $f\left( X,\,Y \right)$, $g\left( X,\,Y \right)$, $h\left( X \right)$ be polynomials with integer coefficients. In this paper we deal with the curve $f{{\left( X,\,Y \right)}^{\text{q}}}\,=\,h\left( X \right)g\left( X,\,Y \right)$ , and we show that under some favourable conditions it is possible to determine all of its rational points.

Keywords

11G3014G0514G25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 1 , 01 March 2009 , pp. 117 - 126
Copyright
Copyright © Canadian Mathematical Society 2009

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