Let $n \in \mathbb{Z}_{\ge 0}$, let $x_0,x_1,\dots,x_n \in \mathbb{R}$ be pairwise distinct, and let $y_0,y_1,\dots,y_n \in \mathbb{R}$. For each $i \in \{0,1,\dots,n\}$, define $\ell_i \in \mathbb{R}[t]$ by
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\begin{align*}
\ell_i(t)=\prod_{\substack{0 \le j \le n, j \ne i}}\frac{t-x_j}{x_i-x_j},
\end{align*}
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with the empty product interpreted as $1$ when $n=0$. Then there exists a unique polynomial $p \in \mathbb{R}[t]$ of degree at most $n$ such that $p(x_i)=y_i$ for every $i \in \{0,1,\dots,n\}$. This polynomial is