A Cauchy-like functional equation (Q1271578)

The author solves the functional equation \[ G(xy-yz)=G(xy-zx)+G(zx-yz)\tag{*} \] for functions \(G\) from the ring of integers into an abelian group, showing that any such function must be a linear combination of four specified functions: the identity function and particular solutions of three simple conditional Cauchy equations. (As a consequence, every such \(G\) satisfies \(G(x+60)=G(x)+G(60)\).) Two corollaries give the general solutions of (*) on prime fields and on the rational field. This gives a different proof of some of the results found in a paper of \textit{J. K. Chung}, \textit{B. R. Ebanks}, \textit{C. T. Ng}, \textit{P. K. Sahoo}, and \textit{W. B. Zeng} [Result Math. 26, No. 3-4, 241-252 (1994; Zbl 0830.39013)].