A solution to the Erdos-Sárközy-Sós problem on asymptotic Sidon bases of order 3

Abstract

A set is a Sidon set if all pairwise sums (for,) are distinct. A set is an asymptotic basis of order 3 if every sufficiently large integer can be written as the sum of three elements of. In 1993, Erdos, Sárközy and Sós asked whether there exists a set with both properties. We answer this question in the affirmative. Our proof relies on a deep result of Sawin on the-Analogue of Montgomery's conjecture for convolutions of the von Mangoldt function.