In this paper we consider a generalized polynomial f : ℝ → ℝ of degree two that satisfies the additional equation f(x)f(y) = 0 for the pairs (x,y) ∈ D, where D ⊆ ℝ2 is given by some algebraic condition. In the particular cases when there exists a positive rational m fulfilling
D = { (x,y) ∈ ℝ2 | x2 - my2 = 1 },
we prove that f(x) = 0 for all x ∈ ℝ.
English