Vol. 118, No. 2, 1985

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Problems and results on additive properties of general sequences. I

Paul Erdős and András Sárközy

Vol. 118 (1985), No. 2, 347–357
Abstract

Let a1 < a2 < be an infinite sequence of positive integers and denote by R(n) the number of solutions of n = ai + aj. The authors prove that if F(n) is a monotonic increasing arithmetic function with F(n) +and F(n) = o(n(log n)2) then |R(n) F(n)| = o((F(n))12) cannot hold.

Mathematical Subject Classification 2000
Primary: 11B34
Secondary: 11B13
Milestones
Received: 12 September 1984
Published: 1 June 1985
Authors
Paul Erdős
András Sárközy