  Let $G$ be a finite nilpotent group, $\chi$ and $\psi$ be irreducible complex
characters of $G$ of prime degree. Assume that $\chi(1)=p$. Then either the
product $\chi\psi$ is a multiple of an irreducible character or $\chi\psi$ is
the linear combination of at least $\frac{p+1}{2}$ distinct irreducible
characters.
