On the solutions of a functional equation attaining transcendental numbers only

We investigate the functional equation f(f(x+y))=f(x+y)+f(x)f(y),\ x,y∈ R. f ( f ( x + y ) ) = f ( x + y ) + f ( x ) f ( y ) , x , y ∈ R . Given a real number c≠ 0, c ≠ 0 , it was shown in [5] that there is a non-trivial solution f with $$f(0)=c$$ f ( 0 ) = c iff c is transcendental and $$>-1$$ > - 1 . In that case all values of f are transcendental. In this paper we find all solutions of the functional equation, discuss their odd properties and the connection with ideals in a group algebra.