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On the Rational Points of the Curve $f(X,Y)^q = h(X)g(X,Y)$ |
Canad. Math. Bull. 52(2009), 117-126
Published:2009-03-01
Printed: Mar 2009
Printed: Mar 2009
- Dimitrios Poulakis
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 |