A certain property of polynomials
type: Item
instance of: scholarly article
title: A certain property of polynomials
zbMATH Open document ID: 0541.12011
DOI: 10.1007/BF02189619
author: N. E. Zubov
published in: Aequationes Mathematicae
publication date: 1982-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/136967
review text: This paper is devoted to the study of polynomials f which satisfy an equation \(f(\alpha x+\beta)=f(x)\) where \(\alpha\) and \(\beta\) are given. Suppose that \(f(\alpha x+\beta)=f(x).\) If \(\alpha \neq \pm 1\) and \(\deg f\geq 3,\) then \(f(x)=(x+\beta /(\alpha -1))^ n+C,\) where \(\alpha\) is an nth root of unity, \(\beta\) and C are constants. Two more results are also established.
Mathematics Subject Classification ID: 12E05
Mathematics Subject Classification ID: 12E12
Mathematics Subject Classification ID: 11R16
Mathematics Subject Classification ID: 11R27
zbMATH DE Number: 3859258
zbMATH Keywords: fundamental unit of cubic field
zbMATH Keywords: equation for polynomials
MaRDI profile type: Publication
cites work: Q3729016
OpenAlex ID: W4234859718
description: scientific article; zbMATH DE number 3859258