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

Table of contents
- Solution b

Solution

Apply the Szemerédi theorem with density

ε

and progression length five. For all sufficiently large

n

, the set

A

contains a nonconstant five-term arithmetic progression

e - 2 r, e - r, e, e + r, e + 2 r,

where

r \neq = 0

a = e - 2 r, b = e - r, c = e + r, d = e + 2 r .

These four elements and

e

are distinct, and direct addition gives

a + b + c + d = (e - 2 r) + (e - r) + (e + r) + (e + 2 r) = 4 e .

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version