2021/03/18 by Kiss, Sándor Z., Sándor, Csaba
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2103.10349
Let k ≥ 2 be an integer. We say a set A of positive integers is an asymptotic basis of order k if every large enough positive integer can be represented as the sum of k terms from A. A set of positive integers A is called Sidon set if all the two terms sums formed by the elements of A are different. Many years ago P. Erdős, A. Sárközy and V. T. Sós asked whether there exists a Sidon set which is asymptotic basis of order 3. In this paper we prove the existence of a Sidon set A with positive lower density of the three fold sumset A + A + A by using probabilistic methods.