Criterion of existence of universal polynomials for the class of linear functions

Recieved: 02/21/2024

Accepted: 06/25/2024

Published: 01/31/2025

Keywords: generation, universal function, sum modulo, polynomial

To cite this article

Voronenko A.A., Sedova A.S. Criterion of existence of universal polynomials for the class of linear functions. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics 2025. N 1. p.31-34 https://doi.org/10.55959/MSU/0137–0782–15–2025–49–1–31–34.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Voronenko A.A. (Lomonosov Moscow State University (MSU))
Sedova A.S. (Lomonosov Moscow State University (MSU))

Abstract

It was proved earlier that product xy is a universal function for the class of linear functions depending on two arguments if k = 6l ± 1. In the paper we prove that there is no universal polynomials for the class of linear functions depending on two arguments for any k dividing three. Also we show that there is no universal
polynomials for the class of linear functions depending on three arguments for any even k. Thus the criterion of existence of universal polynomials for the class of linear functions is obtained.