Published: 2023-10-26

An alternative equation for generalized polynomials of degree two

Zoltán Gábor Boros Logo ORCID , Rayene Menzer Logo ORCID

Abstract

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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Citation rules

Boros, Z. G., & Menzer, R. (2023). An alternative equation for generalized polynomials of degree two. Annales Mathematicae Silesianae, 38(2), 214–220. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/15499

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


ISSN: 0860-2107
eISSN: 2391-4238
Ikona DOI 10.1515/amsil

Publisher
University of Silesia Press

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