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.
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Vol. 38 No. 2 (2024)
Published: 2024-07-23
10.2478/amsil