Autour de f(x)f(y)-f(xy) (Q796001)

The author gives the general real solution of \(f(x)f(y)-f(xy)=h(x+y).\) If \(h(x)\equiv 0,\) this is a classical Cauchy equation. If \(h(x)\not\equiv 0,\) the author proves that f is either constant or \(f(x)=x+a\) (a an arbitrary constant). Partly for the purpose of proving this, the author solves also the equation \(g(x)g(y)+g(x)+g(y)=g(xy)+ag(x+y).\) Remarks deal with generalizations to fields of characteristics different from 2.