Parametrizing over Z integral values of polynomials over Q


Given a polynomial f ∈ Q[X] such that f(Z) ⊂ Z, we investigate whether the set f(Z) can be parametrized by a multivariate polynomial with integer coefficients, that is, the existence of g ∈ Z[X1, . . . , Xm] such that f(Z) = g(Z). We offer a necessary and sufficient condition on f for this to be possible. In particular it turns out that some power of 2 is a… (More)