# Primitivity Rules

**Number Theory**Level 4

For any positive integer \(n\), we define the cyclotomic polynomial \(\Phi_n(x)=\prod(x-w)\), where the product is taken over all primitive nth roots of unity, \(w\). What can we say about the coefficients of the cyclotomic polynomials?

Extra Credit Question: Does the number 2 appear as a coefficient of a cyclotomic polynomial?