\begin{definition}[Definition:Power Sum]
Let $S$ be a finite set of numbers.
Let $p \in \R$ be a real number.
Then the '''$p$th power sum''' of $S$ is defined as:
:$S_p = \ds \sum_{x \mathop \in S} x^p$
That is, it is the summation of the $p$th powers of all the elements of $S$.
\end{definition}