Abstract
A set A is called universal sum-free if, for every finite 0–1 sequence χ = (e1, …, en), either(i) there exist i, j, where 1[les ]j<i[les ]n, such that ei = ej = 1 and i − j∈A, or(ii) there exists t∈N such that, for 1[les ]i[les ]n, we have t + i∈A if and only if ei = 1.It is proved that the density of each universal sum-free set is zero, which settles a problem of Cameron.
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