Exercise 13, § 1

Let $R$ be a reduced root system. $(\alpha_1, \ldots, \alpha_l)$ a basis of $R$ and $\alpha = c_1 \alpha_1 + \cdots + c_l \alpha_l$ a root. Then, $c_i (\alpha_i | \alpha_i) / (\alpha | \alpha) \in \mathbf{Z}$ for all $i$. (Consider the inverse system.)