Linear sets with five distinct differences among any four elements (Q1892854)

A Sidon set \(S\) (or a \(B_2\)-sequence) is a set of real numbers such that the sums of pairs of numbers from \(S\) are all distinct. The following generalization is proposed: a finite set of real numbers is a \((4, 5)\)-set if every \(4\)-subset determines at least \(5\) distinct differences of pairs. Lower and upper bounds for the size of such a set are derived under the assumption that the set contains a certain Sidon set.