Power Functions on the Integers

Question

Suppose $f:\mathbb{R}\to\mathbb{R}$ is of the form $f(x)=x^a$ for some $a\in\mathbb{R}^{+}$. If $f(\mathbb{Z})\subset\mathbb{Z}$, show that $a\in\mathbb{Z}$.

Source: A friend posed this problem; not sure if it is well known.