A nonlinear version of Roth's theorem for sets of positive density in the real line
The author proves that given \(\epsilon >0\) there is a \(\delta (\epsilon)>0\) such that if S is a measurable subset of [0,N], \(| S| >\epsilon N\), then there exist \(a<b<c\) in S satisfying \((c-b)=(b- a)^ 2\) and \(b-a>\delta (\epsilon)\sqrt{N}\).
scientific article; zbMATH DE number 4105556