Problem 245

Let $A\subseteq \mathbb{N}$ be an infinite set such that $\lvert A\cap \{1,\ldots,N\}\rvert=o(N)$ . Is it true that

\limsup_{N\to \infty}\frac{\lvert (A+A)\cap \{1,\ldots,N\}\rvert}{\lvert A\cap \{1,\ldots,N\}\rvert}\geq 3?

Source: erdosproblems.com/245

Additive combinatorics

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An accepted solution exists. The statement is true.

Proved, the site's label: the answer is yes, by the theorem of Freĭman's 1973 monograph [Fr73], recorded on its claim page (Freiman, 1973) with the site's acceptance as its only evidence. The label carries no Lean qualification; a Lean development in Boris Alexeev's lean-proofs repository that declares itself a formalization of Freĭman's solution is linked from the claim page and has not been built or audited by this corpus.

Problem 245

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