Solving Genus Zero Diophantine Equations with at Most Two Infinite Valuations

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.