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Erdős problem 487

Let A⊆NA\subseteq \mathbb{N} have positive density. Must there exist distinct a,b,c∈Aa,b,c\in A such that [a,b]=c[a,b]=c (where [a,b][a,b] is the least common multiple of aa and bb)?

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/487.lean

Formal Conjectures

FormalConjectures/ErdosProblems/487.leanErdos487.erdos_4871 lineExact file
True ↔ ∀ (A : Set ℕ), A.HasPosDensity → ∃ a ∈ A, ∃ b ∈ A, ∃ c ∈ A, a ≠ b ∧ b ≠ c ∧ a ≠ c ∧ a.lcm b = c
SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

Proof manifests naming this Problem

  • Jayyhk Erdős Leanjayyhk:erdos:487
  • PLBY Lean proofsErdosProblems.Erdos487

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

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