integrality of certain rational numbers Let $P,Q\in\mathbb Q[X]$ be relatively prime polynomials ($X$ being an indeterminate). Assume that $Q(0)=1$ and that $P/Q$ is in $\mathbb Z[[X]]$. 
Does this imply that $P$ and $Q$ are in $\mathbb Z[X]$?

This is a straightforward consequence of Fatou's Lemma on rational power series. Here is a statement and proof from R. P. Stanley's Enumerative Combinatorics, I (or see p. 629 of the free version here)


