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Density of \(M\)-sets in arithmetic progression. (English) Zbl 0932.11009

Given a set \(M\) of positive integers, a set \(S\) of non-negative integers is called an \(M\)-set if \(a,b,\in S\) implies \(a-b\notin M\). Motzkin posed the problem of determining \(\mu(M)=\sup_S\overline{\delta}(S)\), where the supremum is taken over the class of all \(M\)-sets and \(\overline{\delta}(S)\) denotes the upper asymptotic density. In the note an explicit formula for \(\mu(M)\) is given in the case when \(M\) is a finite arithmetic progression.

MSC:

11B05 Density, gaps, topology
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