I was reading about cyclotomic polynomials defined as:
$$ \Phi_n(x) = \prod_\stackrel{1\le k\le n}{\gcd(k,n)=1} \left(x-e^{2i\pi\frac{k}{n}}\right)$$
The fact that the coefficients of these polynomials are integers has a consequence (just looking at constant coefficient of the polynomial) which is simple to state:
$$n | \left( \sum_{1\le k<n, \gcd(k,n)=1} k \right)$$
However, is there a more elementary proof of this second statement ?
