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  • Autor
    • Elsholtz, Christian
    • Planitzer, Stefan
  • TitelOn Erdős and Sárközy's sequences with Property P
  • Datei
  • DOI10.1007/s00605-016-0995-9
  • Persistent Identifier
  • Erschienen inMonatshefte für Mathematik
  • Band182
  • Erscheinungsjahr2017
  • Heft3
  • Seiten565-575
  • ISSN1436-5081
  • ZugriffsrechteCC-BY
  • Download Statistik364
  • Peer ReviewJa
  • AbstractA sequence A of positive integers having the property that no element \(a_i \in A\) divides the sum \(a_j+a_k\) of two larger elements is said to have `Property P'. We construct an infinite set \(S \subset \mathbb{N}\) having Property P with counting function \(S(x) \gg \frac{\sqrt{x}}{\sqrt{\log x}(\log\log x)^2(\log\log\log x)^2}\) . This improves on an example given by Erdős and Sárközy with a lower bound on the counting function of order \(\frac{\sqrt{x}}{\log x}\).