On Sidon sets which are asymptotic bases

Abstract

Let h 2 be an integer. We say that a set A of positive integers is an asymptotic basis of order h if every large enough positive integer can be represented as the sum of h terms from A. A set of positive integers A is called a Sidon set if all the sums a + b with a ∈A , b ∈A , a b, are distinct. In this paper we prove the existence of Sidon sets which are asymptotic bases of order 5 by using probabilistic methods.