Let $A \subseteq {1, \dots, N}$ be such that there are no $a, b, c \in A$ such that $a ∣ (b + c)$ and $a < min (b, c)$ . Is it true that $∣ A ∣ \leq N /3 + O (1)$ ?

Worked, still open.

number theory · solved · prize $100 · formalized (Lean) · 0 attempts

machinery: consecutive-integer-window,additive-combinatorics,g_kr-divisors,extremal-set-system,prime-distribution

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

formal

AMS 5 11 · solved (literature)

theorem erdos_13 : ∃ C : ℝ, ∀ N : ℕ, ∀ A ⊆ Icc 1 N, IsForbiddenTripleFree A →
    (A.card : ℝ) ≤ (N : ℝ) / 3 + C

solved