On two additive problems

Paul Erdos, Gregory Freiman

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Abstract

Denote by A a set of x different natural numbers. The following two results are obtained: 1. (1) For sufficiently large x and A ⊂ [1, 3x - 3] there exists a subset B ⊂ A such that for some l ∈ Z ∑ aiε{lunate}B ai=2l 2. (2) For sufficiently large x and A ⊂ [1, 4x - 4] there exists a subset B ⊂ A such that Σai ∈ B ai is a square-free number.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalJournal of Number Theory
Volume34
Issue number1
DOIs
Publication statusPublished - Jan 1990

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ASJC Scopus subject areas

  • Algebra and Number Theory

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