About a polynomial with complex coefficients taking integer values for sufficiently large integers Let $f(x)$ be a polynomial with complex coefficients such that $\exists n_0 \in \mathbb Z^+$ such that $f(n) \in \mathbb Z , \forall n \ge n_0$, then is it true that $f(n) \in \mathbb Z , \forall n \in \mathbb Z$ ?

Proof by induction on the degree of the polynomial. Trivially true for degree zero. Assume true for degree $n$. Let $f$ have degree $n+1$ and be integral for all sufficiently large integer arguments. Then same is true for $g(x)=f(x+1)-f(x)$, a polynomial of degree $n$. By the induction hypothesis, $g$ is integer-valued for all integer arguments. Then it follows that $f$ is. 
