I am required to prove the following (which I believe was originally a result of Migotti):
Let $p,q$ be distinct primes. Show that the $pq$th cyclotomic polynomial has coefficients all -1, 0 or 1. Show moreover that if n is a product of at most two distinct primes then the $n$th cyclotomic polynomial has coefficients -1,0 or 1.
I have got an expression for the $pq$ case of $\frac{\Phi_q(t^p)}{\Phi_q(t)}$ where $\Phi_q(t) = 1+t+t^2+...+t^{q-1}$. I could slog through dividing that out, but it won't be pretty. I'm wondering if there is some deeper connection with Sylow theory that I could use, as the conditions look somewhat reminiscient of conditions on group order. Is it possible to formulate this usefully as a Sylow Theory problem?