An improvement of a theorem of Erdős and Sárközy

Horváth, Gábor (2007) An improvement of a theorem of Erdős and Sárközy. Pollack Periodica, 2 (Supple). pp. 155-161. ISSN 1788-1994

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Abstract

Let 12 ... a a< <be an infinite sequence of positive integers and denote by ()2R nthe number of solutions of i jn a a= +. P. Erdıs and A. Sárközy proved that if ()g n is a monotonically increasing arithmetic function with ()g n→ +∞ and ( )( )()2logg n o n n−= then ( ) ( )( )()2R n g n o g n−= cannot hold. We will show that for any 0ε>, the inequality ( ) ( )( ) ( )21R n g ng nε−≤ − cannot hold from a certain point on.

Item Type:	Article
Uncontrolled Keywords:	Additive number theory, General sequences, Additive representation function
Divisions:	Informatika Intézet > Matematikai és Számítástudományi Tanszék
Depositing User:	Gergely Beregi
Date Deposited:	23 Jun 2021 09:06
Last Modified:	23 Jun 2021 09:06
URI:	http://publication.repo.uniduna.hu/id/eprint/782
MTMT:	1491227

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