On the functional equation x plus f(y plus f(x))=y plus f(x plus f(y))

For an abelian group (G, + ,0) we consider the functional equation f : G -> G, x + f(y + f(x)) = y + f(x + f(y)) (for all x, y is an element of G), (1) most times together with the condition f(0) = 0. (0) Our main question is whether a solution of (1) boolean AND (0) must be additive, i.e., an endomorphism of G. We shall answer this question in the negative (Example 3.14) Ratz (Aequationes Math 81:300, 2011).