%0 Journal Article
%T Polynomial parametrization of the solutions of Diophantine equations of genus 0
%A Sophie Frisch
%A G¨šnter Lettl
%J Mathematics
%D 2008
%I arXiv
%X Let f in Z[X,Y,Z] be a non-constant, absolutely irreducible, homogeneous polynomial with integer coefficients, such that the projective curve given by f=0 has a function field isomorphic to the rational function field Q(t). We show that all integral solutions of the Diophantine equation f=0 (up to those corresponding to some singular points) can be parametrized by a single triple of integer-valued polynomials. In general, it is not possible to parametrize this set of solutions by a single triple of polynomials with integer coefficients.
%U http://arxiv.org/abs/0812.0330v1