The board / number theory / #13
Erdős Problem #13
PROVED LEANdatabase updated 2026-08-23
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
A finite set of naturals `A` is said to be forbidden-triple-free if for all `a, b, c ∈ A`, if `a < min(b, c)` then `a` does not divide `b + c`.
If \(A \subseteq \{1, ..., N\}\) is a set with no \(a, b, c \in A\) such that \(a | (b+c)\) and \(a < \min(b,c)\), then \(|A| \le N/3 + O(1)\). This has been solved by Bedert [Be23]. [Be23] Bedert, B., _On a problem of Erdős and Sárközy about sequences with no term dividing the sum of two larger terms_. arXiv:2301.07065 (2023).
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/13.Prize$100
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanyes
OEISA002264
Original pageerdosproblems.com/13
Attempts
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