I'm very bad in computations of this kind :/. I don't know tricks for computing the discriminant of a polynomial, only the definition and using the resultant, but it's very complicated to do only with that tools. I need some help please ._.
I have to prove that the discriminant of $\Phi_p$ is $ (-1)^{\frac{p-1}{2}}p^{p-2}$ I don't know if it's neccesary to assume that $p$ is prime.