A note on the density of sum-free sets
Obviously, each set \(A\) of upper density larger than \({1\over 2}\) contains two different elements \(x,y\) such that \(x+ y\in A\) (it is enough to take any \(x\in A\) and \(y\in A\cap(A- x)\)). On the other hand, the set of all odd numbers is sum-free and has density \({1\over 2}\). In this note we shall prove that this set is, in a way, the unique extremal set for this property, i.e., the ``threshold density'' of the property that set \(A\) is sum-free drops down to \({2\over 5}\) under the assumption that \(A\) contains at least one even number.
scientific article; zbMATH DE number 753623