The <Balog-Szemerédi-Gowers theorem> states that if a finite set $A$ has at least $\delta|A|^3$ <additive quadruples>, then it has a subset $A'\subseteq A$ such that
$$
|A'|\geq\delta^C|A|,
\qquad
|A'+A'|\leq\delta^{-C}|A'|,
$$
where $C$ is an absolute constant.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 129 / 4 / d / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-129/4/d/solution