Le problème facile de Waring. (The easier Waring problem)
type: Item
instance of: scholarly article
title: Le problème facile de Waring. (The easier Waring problem)
zbMATH Open document ID: 0759.11034
author: Philippe Revoy
published in: L'Enseignement Mathématique. 2e Série
publication date: 1992-09-26T00:00:00Z
review text: In this Waring problem, the knowledge of the function \(\nu(k)\) [the smallest integer \(s\) such that every integer is the sum of \(s\) integers of the form \(\pm z^ k\), \(z\) an integer] is far from precise. Except for the trivial majoration \(G(k)+1\) \([G(k)\) being the asymptotic constant associated with the Waring problem], there are only large majorations for small \(k\). Here the author gives classical facts and the particular cases \(k=4\) and \(k=5\). Then certain new identities are presented which arose in a paper of \textit{L. N. Vaserstein} [J. Number Theory 28, 66-68 (1988; Zbl 0634.10042)], who gave a better bound for \(\nu(8)\). A short description of the Tarry-Escott problem is given, which is, for \(k\geq 9\), the only way to get effective majorations of \(\nu(k)\).
reviewed by: Edward L. Cohen
Mathematics Subject Classification ID: 11P05
zbMATH DE Number: 55791
zbMATH Keywords: easier Waring problem
zbMATH Keywords: identities
zbMATH Keywords: Tarry-Escott problem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 55791