On the equation P(f) = Q(g), where P,Q are polynomials and f , g are entire functions

In 1922 Ritt described polynomial solutions of the functional equation P( f) = Q(g). In this paper we describe solutions of the equation above in the case when P,Q are polynomials while f , g are allowed to be arbitrary entire functions. In fact, we describe solutions of the more general functional equation s = P( f) = Q(g), where s, f , g are entire functions and P,Q are arbitrary rational functions. As an application we solve the problem of description of "strong uniqueness polynomials" for entire functions.