On the functional equation $F(A(z))=G(B(z)),$ where $A,B$ are   polynomial$ and $F,G$ are continuous functions
  In this note we describe solutions of the equation: $F(A(z))=G(B(z)),$ where $A,B$ are polynomials and $F,G$ are continuous functions on the Riemann sphere. 
Fedor Pakovich