Sumsets containing infinite arithmetic progressions

Paul Erdös, Melvyn B. Nathanson, András Sárközy

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Let A be a set of nonnegative integers such that dL(A) = w > 0. Let k be the least integer satisfying k ≥ 1 w. It is proved that there is an infinite arithmetic progression with difference at most k + 1 such that every term of the progression can be written as a sum of exactly k2 - k distinct terms of A, and there is an infinite arithmetic progression with difference at most k2 - k such that every term of the progression can be written as a sum of exactly k + 1 distinct terms of A. A solution is also obtained to the infinite analog of a problem of Erdös and Freud on powers of 2 and on square-free numbers that can be represented as bounded sums of distinct elements chosen from a set A with positive density.

Original languageEnglish
Pages (from-to)159-166
Number of pages8
JournalJournal of Number Theory
Volume28
Issue number2
DOIs
Publication statusPublished - Feb 1988

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ASJC Scopus subject areas

  • Algebra and Number Theory

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