Kurepa's functional equation on semigroups.
The functional equation to which the title refers is:F(x,y) + F(xy,z) = F(x,yz) + F(y,z),where x, y and z are in a commutative semigroup S and F: S x S --> X with (X,+) a divisible abelian group (Divisibility means that for any y belonging to X and natural number n there exists a (unique) solution x belonging to X to nx = y).