Source labels openChecked July 26, 2026

Erdős Problem 287

Let $k\geq2$ . Is it true that, for any distinct integers $1 < n_1 < \cdots < n_k$ such that $\sum_{i=1}^k \frac{1}{n_i} = 1$ , we must have $\max(n_{i+1} - n_i) \geq 3$ ?

Number theory AMS 11

Mathematical statement

Let $k\geq2$ . Is it true that, for any distinct integers $1 < n_1 < \cdots < n_k$ such that $\sum_{i=1}^k \frac{1}{n_i} = 1$ , we must have $\max(n_{i+1} - n_i) \geq 3$ ?

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_287

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_287 : answer(sorry) ↔    ∀ (k : ℕ) (hk : 2 ≤ k) (s : Fin k → ℕ),    StrictMono s → 1 < s ⟨0, by omega⟩ →    ∑ i : Fin k, 1/ (s i : ℝ) = 1 →    3 ≤ max_gap k s:= by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization erdosproblems.com/287background