I was working on a problem, I need to show that a certain type of equation has a unique solution. By Cramer's Rule the problem reduces to:

$\displaystyle \left| \begin{array}{ccccc} 1^0&2^0&3^0&....&n^0\\ 1^1&2^1&3^1&....&n^1\\1^2&2^2&3^2&....&n^2\\....&. ...&....&....&....\\1^n&2^n&3^n&....&n^n \end{array} \right| \not = 0$

I asked my teacher he said there is a name for it, but did not know much about it. Someone know what this is? Or how to prove it?