Let a1 2 k (n) the number of solutions of n = ai1 + ai2 +...+a ik. P. Erdos and A. Sárközy proved that if F(n) is a monotonie increasing arithmetic function with F(n) → +∞ and F(n) = o(n(log n)-2) then |R2...
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Let h, k >= 2 be integers. 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 ...
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Let h, k >= 2 be integers. 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 a B-h[g] set if every positive integer can be represented as the sum of h terms from A in at most g different ways. In this paper we prove the existence of B-h[1] sets which are asymptotic bases of order 2h + 1 by using probabilistic methods. (C) 2020 The Authors. Published by Elsevier B.V.
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