Solving genus zero diophantine equations with at most two infinite valuations

Authors:
Dimitrios Poulakis;Evaggelos Voskos
Affiliations:
Univ. of Thessaloniki, Greece;Univ. of Thessaloniki, Greece
Venue:
Journal of Symbolic Computation
Year:
2002

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Abstract

Let f(X, Y) be an absolutely irreducible polynomial with integer coefficients such that the curve defined by the equation f(X, Y) = 0 is of genus 0 having at most two infinite valuations. This paper describes a practical general method for the explicit determination of all integer solutions of the diophantine equation f(X, Y) = 0. Several elaborated examples are given. Furthermore, a necessary and sufficient condition for a curve of genus 0 to have infinitely many integer points is obtained.