A Goldbach 3-primes theorem for polynomials of low degree over finite fields of characteristic 2
type: Item
instance of: scholarly article
title: A Goldbach 3-primes theorem for polynomials of low degree over finite fields of characteristic 2
zbMATH Open document ID: 0653.12009
DOI: 10.1016/0022-314X(88)90111-4
author: Gove Effinger
published in: Journal of Number Theory
publication date: 1988-01-01T00:00:00Z
review text: A monic polynomial M in one variable x over the finite field \({\mathbb{F}}_ q\) is called even if \(q=2\) and if x or \(x+1\) divides M; otherwise M is called odd. In this paper the author proves that every odd monic polynomial M of degree 2, 3, 4, 5, and 6 over every finite field \({\mathbb{F}}_ q\) of characteristic 2 can be written as a sum of three irreducible monic polynomials except in case \(M(x)=x^ 2+a\), \(a\in {\mathbb{F}}_ q\).
Mathematics Subject Classification ID: 11T06
Mathematics Subject Classification ID: 11P99
zbMATH DE Number: 4065119
zbMATH Keywords: Goldbach theorem
zbMATH Keywords: monic polynomial
zbMATH Keywords: finite field
zbMATH Keywords: characteristic 2
MaRDI profile type: Publication
cites work: Q3228640
cites work: A Goldbach theorem for polynomials of low degree over odd finite fields
cites work: The expression of a polynomial as a sum of three irreducibles
cites work: Q4001344
cites work: Q5690468
description: scientific article; zbMATH DE number 4065119