Golomb's conjectures and related problems
type: Item
instance of: scholarly article
title: Golomb's conjectures and related problems
zbMATH Open document ID: 0844.11079
published in: Chinese Science Bulletin
publication date: 1995-11-16T00:00:00Z
review text: The conjectures of \textit{S. Golomb} [J. Comb. Theory, Ser. A 37, 13-21 (1984; Zbl 0547.05020)]\ concern the representability of elements of a finite field as sums of two primitive elements. Using tools from analytic number theory, the author obtains an asymptotic formula for the number of such representations in the special case of finite fields \(GF(p)\), \(p\) an odd prime. As a corollary, the Golomb conjectures hold in \(GF(p)\) if \(p-1\) does not have too many prime divisors.
Mathematics Subject Classification ID: 11T30
Mathematics Subject Classification ID: 12E20
zbMATH DE Number: 817773
zbMATH Keywords: representability
zbMATH Keywords: sums of two primitive elements
zbMATH Keywords: asymptotic formula
zbMATH Keywords: Golomb conjectures
author: Wenpeng Zhang
reviewed by: Theo Grundhöfer
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 817773