Anyone having any ideas about how this formula could be proved?(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\underset{k<l}{\prod_{k,l=1}^n} (x_k - x_l) = (-1)^{n(n-1)/2} \left|\begin{array}{ccc}

1 & \cdots & 1 \\

x_1 & \cdots & x_n \\

\vdots & & \vdots \\

x_1^{n-1} & \cdots & x_n^{n-1} \\

\end{array}\right|

[/tex]

I tried induction without success. The induction step seems to only require other difficult formulas.

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# Difficult polynomial and determinant formula

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