On Erdős and Sárközy’s sequences with Property P

Abstract

A 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 Erd\H{o}s and S\'ark\"ozy with a lower bound on the counting function of order $\frac{\sqrt{x}}{\log x}$.

Locations

• Monatshefte für Mathematik - View - PDF
• arXiv (Cornell University) - View - PDF
• TUGraz OPEN Library (Graz University of Technology) - View - PDF
• DataCite API - View