On divisibility properties of integers of the forma+á

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1987 English Publisher:Springer Science and Business Media LLCJournal:Acta Mathematica Hungarica, volume 50, pages 117-122 (issn: 0236-5294, eissn: 1588-2632,

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Authors: Erdős, Paul; Sárközy, A.;

doi: 10.1007/bf01903370

On divisibility properties of integers of the forma+á

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Abstract

Let \(A\subseteq \{1,2,...,N\}\) be such that \(a+a'\) for \(a\in A\), \(a'\in A\) be all square-free. Then the authors prove the following interesting results. Theorem 1. For \(N>N_0\) there exists an \(A\) such that \(|A| > (1/248)\log N.\) Theorem 2. For \(N>N_1\) every \(A\) satisfies \(|A| cN\), \(|B|\to\infty\) is possible.

Related Organizations

Hungarian Academy of Sciences
Hungary

Keywords

\(k\)-free integers, Special sequences and polynomials, arithmetic properties, Sieves, large sieve, sums of sequences of integers, square-free integers

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