18.20 (2014)

Characters $\varphi$ and $\psi$ of a finite group $G$ are said to be semiproportional if they are not proportional and there is a normal subset $M$ of $G$ such that $\varphi|_M$ is proportional to $\psi|_M$ and $\varphi|_{G \setminus M}$ is proportional to $\psi|_{G \setminus M}$.
Conjecture: If $\varphi$ and $\psi$ are semiproportional irreducible characters of a finite group, then $\varphi(1) = \psi(1)$.