Problems and results on additive properties of general sequences. V
type: Item
instance of: scholarly article
title: Problems and results on additive properties of general sequences. V
zbMATH Open document ID: 0597.10055
DOI: 10.1007/BF01294598
author: Vera T. Sós
author: András Sárközy
author: P. Erdős
published in: Monatshefte für Mathematik
publication date: 1986-01-01T00:00:00Z
review text: [Part I, cf. Pac. J. Math. 118, 347--357 (1985; Zbl 0569.10032), part IV, cf. Lect. Notes Math. 1122, 85--104 (1985; Zbl 0588.10056).] A very special case of one of the theorems of the authors states as follows: Let \(1\leq a_1\leq a_2\leq\dots\) be an infinite sequence of integers for which all the sums \(a_i+a_j\), \(1\leq i\leq j\), are distinct. Then there are infinitely many integers \(k\) for which \(2k\) can be represented in the form \(a_i+a_j\) but \(2k+1\) cannot be represented in this form. Several unsolved problems are stated.
Mathematics Subject Classification ID: 11B34
Mathematics Subject Classification ID: 11B75
zbMATH DE Number: 3961754
zbMATH Keywords: addition sequences
zbMATH Keywords: infinite sequence of integers
zbMATH Keywords: unsolved problems
Wikidata QID: Q105956450
MaRDI profile type: Publication
cites work: Additive properties of random sequences of positive integers
cites work: Problems and results on additive properties of general sequences. I
cites work: Q3822287
full work available at URL: https://doi.org/10.1007/bf01294598
OpenAlex ID: W2385767858
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description: scientific article; zbMATH DE number 3961754