On the Practical Solution of Genus Zero Diophantine Equations

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 least three 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. Some elaborated examples are given.