On the completeness of an exponential type sequence
type: Item
instance of: scholarly article
title: On the completeness of an exponential type sequence
zbMATH Open document ID: 0952.11003
DOI: 10.1023/A:1006799619623
author: Norbert Hegyvári
published in: Acta Mathematica Hungarica
publication date: 2000-11-13T00:00:00Z
review text: Confirming a conjecture of P. Erdős, in 1959 \textit{B. J. Birch} [Proc. Camb. Philos. Soc. 55, 370-373 (1959; Zbl 0093.05003)] proved that for any coprime integers \(p, q>1\) every sufficiently large integer is a sum of distinct numbers of the form \(p^\alpha q^\beta \). The author shows that summands with the restriction \(\beta \leq K\) suffice for a suitable \(K=K(p,q)\), and exhibits such a bound \(K\). The bound is quadruply exponential in \(p\) and triply in \(q\), probably not the true order of magnitude.
reviewed by: Imre Z. Ruzsa
Mathematics Subject Classification ID: 11B83
Mathematics Subject Classification ID: 11B75
zbMATH DE Number: 1528632
zbMATH Keywords: complete sequences
MaRDI profile type: Publication
full work available at URL: a:1006799619623
OpenAlex ID: W1636213170
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description: scientific article; zbMATH DE number 1528632