Problems and results on additive properties of general sequences. I

Paul Erdős and András Sárközy

Vol. 118 (1985), No. 2, 347–357

DOI: 10.2140/pjm.1985.118.347

Abstract

Let a₁ < a₂ < ⋯ be an infinite sequence of positive integers and denote by R(n) the number of solutions of n = a_i + a_j. 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))^1∕2) cannot hold.

Mathematical Subject Classification 2000

Primary: 11B34

Secondary: 11B13

Milestones

Received: 12 September 1984

Published: 1 June 1985