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On a Problem of Erdős and Sárközy

✍ Scribed by Tomasz Schoen

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 89 KB
Volume: 94
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.2000.3142

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✦ Synopsis

Let A=[a 1 , a 2 , ...] N and put A(n)= a i n 1. We say that A is a P-set if no element a i divides the sum of two larger elements. It is proved that for every P-set A with pairwise co-prime elements the inequality A(n)<2n 2Â3 holds for infinitely many n # N.

2001 Academic Press

where A(n)= a i n 1. (If one replaces the condition x, y>z by x{z, y{z then (2) becomes a simple consequence of a well-known result of Roth [4].) Furthermore, they showed [2] that (2) cannot be substituted by any effective bound, however, they conjectured that there exists a positive constant c such that A(n)<n 1&c ,

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