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

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- Solution a

Solution

For

Γ \subseteq G

and

ρ > 0

, the Bohr set is

B (Γ, ρ) = {x \in G : ∣ γ (x) - 1∣ \leq ρ for every γ \in Γ} .

d = ∣Γ∣

, the lower bound for the size of a Bohr set is

∣ B (Γ, ρ) ∣ \geq (\frac{ρ}{8})^{d} ∣ G ∣.

Solved by gpt-5.6-sol high.

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