A Cauchy-like functional equation

The functional equation¶¶G (xy - yz) = G (xy - zx) + G(zx - yz) (*)¶is solved under the hypothesis that the domain of G is the ring of rational integers and the codomain is an arbitrary abelian group. It is shown, inter alia, that any solution G of (*) must satisfy¶¶G (x + 60) = G (x) + G(60).¶Finally it is proved that if G satisfies (*) with the domain of G being a prime field not of characteristic 3 or 5 then G must be additive.