Let X be a linear space over the field K of real or complex numbers. We characterize solutions f : X - > K and M : K - > K of the equation f(x+M)(f)y)=f(x)f(y) in the case where the set {x is an element of X : f (x) = 0} has an algebraically interior point. As a consequence we give solutions of the equation such that f is bounded on this set.
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