Abstract
Let h,k≥2 be integers. A set A of positive integers is called asymptotic basis of order k if every large enough positive integer can be written as the sum of k terms from A. A set of positive integers A is said to be a Bh[g]-set if every positive integer can be written as the sum of h terms from A at most g different ways. In this paper we prove the existence of Bh[1] sets which are asymptotic bases of order 2h by using probabilistic methods.
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