Erdős problem 13 · problems.science

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].

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FormalConjectures/ErdosProblems/

13.lean

Retained formal statement1 of 2

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).

FormalConjectures/ErdosProblems/13.leanErdos13.erdos_131 lineExact file

1∃ C, ∀ (N : ℕ), ∀ A ⊆ Finset.Icc 1 N, Erdos13.IsForbiddenTripleFree A → ↑A.card ≤ ↑N / 3 + C

SolvedStatement only, no proof

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