Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 129 / 2 / e

Table of contents
- Solution e

Solution

Part c gives

x + B (Γ, α) \subseteq A + A + A

with

d = ∣Γ∣ \leq 2 α^{- 3}

. By the arithmetic progression in a cyclic Bohr set,

B (Γ, α)

contains a centered progression of length at least

\frac{1}{8} α N^{1/ d} \geq \frac{1}{8} α N^{α^{3} /2} .

Its translate by

x

is the required arithmetic progression in

A + A + A

.

Solved by gpt-5.6-sol high.

 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