  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.
