Let $k$ be a field, let $d \in \mathbb{N} \cup \{0\}$, and let $p,q \in k[x]$ satisfy $\deg p \leq d$ and $\deg q \leq d$. Suppose there exist pairwise distinct elements $a_0,\dots,a_d \in k$ such that
paragraph
admin
\begin{align*}
p(a_i)=q(a_i)
\end{align*}
latex_env
admin
for every $i \in \{0,\dots,d\}$. Then $p=q$ in $k[x]$.