- 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
- Download Statistik2086
- 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 \(\frac{\sqrt{x}}{\log x}\).
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