Monomial functions, normal polynomials and polynomial equations

Abstract In this paper we consider generalized monomial functions $$f, g:{\mathbb {F}}\rightarrow {\mathbb {C}}$$ f , g : F → C (of possibly different degree) that also fulfill $$\begin{aligned} f(P(x))= Q(g(x)) \qquad \left( x\in {F}}\right) , \end{aligned}$$ ( P x ) = Q ∈ where $$P\in {F}}[x]$$ [ ] and $$Q\in {C}}[x]$$ are given (classical) polynomials.