\[\begin{vmatrix}1&x_{1}&x^{2}_{1}&\cdots&x^{n-1}_{1}\\
1&x_{2}&x^{2}_{2}&\cdots&x^{n-1}_{2}\\
\vdots&\vdots&\vdots&\ddots&\vdots\\
1&x_{n}&x^{2}_{n}&\cdots&x_{n}^{n-1}\end{vmatrix}=\prod_{1\leq j<k\leq n}(x_{k%
}-x_{j}).\]