For distinct elements $x_1, x_2, \ldots, x_m$ in a field,
\begin{align*}
\det \begin{pmatrix}
1 & 1 & \cdots & 1 \\
x_1 & x_2 & \cdots & x_m \\
\vdots & & & \vdots \\
x_1^{m-1} & x_2^{m-1} & \cdots & x_m^{m-1}
\end{pmatrix}
= \prod_{1 \leq j < i \leq m} (x_i - x_j).
\end{align*}