Exercise 12, § 2

Let $M$ be an $A$-module. Let $\alpha_0, ..., \alpha_n \in A$ be such that, for $i \neq j$, the homothety with ratio $\alpha_i - \alpha_j$ in $M$ is bijective. Whatever $m_0, ..., m_n \in M$ may be, there exists one and only one $f \in M[X]$ such that $f(\alpha_i) = m_i$ for $0 \leq i \leq n$ and $\deg f \leq n$.