Representation of elements of a sequence by sumsets (Q1375703)

Let \(A\) be a finite and \(S\) an infinite set of positive integers. Suppose that \(S\) has an element in the interval \([N, 2N]\) for every positive integer \(N\geq N_0 (\geq1)\). In the paper the author shows that there is an integer \(k\), depending on the density of \(A\), such that some elements of \(S\) can be represented by a sum of at most \(k\) elements of \(A\).