\begin{definition}[Definition:Cyclotomic Polynomial]
Let $n \ge 1$ be a natural number.
The '''$n$th cyclotomic polynomial''' is the polynomial
:$\ds \map {\Phi_n} x = \prod_\zeta \paren {x - \zeta}$
where the product runs over all primitive complex $n$th roots of unity, that is, those whose order is $n$.
\end{definition}