Let $\Phi_n(x)$ be a cyclotomic polynomial, n $\in \mathbb{N}$. Prove that $Disc(\Phi_n(x)) = (-1)^{\frac {\phi(n)}{2}}n^{\phi(n)}\prod_{p|n, p -prime} {p}^{\frac {\phi(n)}{1-p}}$
I've found the solution for prime n. For arbitrary n we have $D(\Phi_n(x))=\prod_{\substack{1\le j<k\le n\\\gcd(j,n)=\gcd(k,n)=1}}(e^{\frac{2k\pi i}{n}}-e^{\frac{2j\pi i}{n}})^2$. Also we have $\Phi_n(X) = \frac{x^n-1}{\prod_{d|n, d<n} \Phi_d(x)}$. What can I get from that?