Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 122 / 3 / b / Solution

Apply the Szemerédi theorem with density $\epsilon$ and progression length five. For all sufficiently large $n$, the set $A$ contains a nonconstant five-term arithmetic progressionwhere $r\ne 0$. SetThese four elements and $e$ are distinct, and direct addition gives

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