Parity of the number of irreducible factors for composite polynomials
type: Item
instance of: scholarly article
title: Parity of the number of irreducible factors for composite polynomials
zbMATH Open document ID: 1200.11092
author: Ryul Kim
author: W. Koepf
published in: Finite Fields and their Applications
publication date: 2010-05-26T00:00:00Z
review text: The focus of the paper is on the parity of the number of irreducible factors of a given polynomial over a finite field. Here the authors consider the discriminants of the composition of some polynomials over a finite field. They establish a relation between the discriminant of the composed one and the original one. They apply this then to obtain results like the following. For any integer \(k>3\), \(k>l\) and \(l\geq 1\), the pentanomial \(f(x)=x^{2^k-1}+x^{2^l+1}+x^{2^l}+x+1\) has always an odd number of irreducible factors over the finite field with two elements.
reviewed by: Pieter Moree
Mathematics Subject Classification ID: 11T06
Mathematics Subject Classification ID: 11T55
zbMATH DE Number: 5712573
zbMATH Keywords: Discriminant
zbMATH Keywords: Stickelberger's theorem
zbMATH Keywords: Swan's theorem
zbMATH Keywords: polynomials
zbMATH Keywords: finite fields
MaRDI profile type: Publication
full work available at URL: j.ffa.2009.12.002
OpenAlex ID: W2008432412
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DOI: 10.1016/J.FFA.2009.12.002
description: scientific article; zbMATH DE number 5712573