The board / additive combinatorics / #245
Erdős Problem #245
PROVEDdatabase updated 2025-08-31
The statement as posed is true, and a proof exists.
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Let \(A\subseteq\mathbb{N}\) be an infinite set such that \(|A\cap \{1, ..., N\}| = o(N)\). Is it true that \[ \limsup_{N\to\infty}\frac{|(A + A)\cap \{1, ..., N\}|}{|A \cap \{1, ..., N\}|} \geq 3? \] The answer is yes, proved by Freiman [Fr73]. [Fr73] Fre\u{\i}man, G. A., _Foundations of a structural theory of set addition_. (1973), vii+108.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/245.Prizenone
Topicsadditive combinatorics
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/245
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