On the equation F(X) + M(X)G(X−1)=0 on Kn

AbstractAll triples F, G, M: Kn → K of additive F, G and multiplicative M satisfying the titular functional equation on (K⧹{0})n, where K is a commutative field of characteristics ≠2, are determined. This generalizes and unifies research arising from problems in two different areas. Ng has solved this problem for n = 1, culminating a succession of results by various authors concerning the Halperin problem on quadratic forms. Also, for K = R (the reals) and G = F this problem arose in a characterization of information measures