On a problem of Z. Daróczy - Jarczyk, Witold (Annales Mathematicae Silesianae, 1991)
Some conditions on F: X→R (X = (0,∞) or X = N) which guarantee that all solutions of the equation F(x) = F(x+1)+F(x(x + 1)) have to be of the form F(x) = F(1)/x are given.