Source labels openChecked July 26, 2026

Erdős Problem 288

Is it true that there are only finitely many pairs of intervals $I_1$ , $I_2$ such that $\sum_{n_1 \in I_1} \frac{1}{n_1} + \sum_{n_2 \in I_2} \frac{1}{n_2} \in \mathbb{N}?$

Number theory AMS 11

Mathematical statement

Is it true that there are only finitely many pairs of intervals $I_1$ , $I_2$ such that

\sum_{n_1 \in I_1} \frac{1}{n_1} + \sum_{n_2 \in I_2} \frac{1}{n_2} \in \mathbb{N}?

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_288

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_288 : answer(sorry) ↔ Set.Finite { I : Fin 2 → ℕ+ × ℕ+ |    ∀ j, (I j).1 ≤ (I j).2 ∧      ∃ n : ℕ+, (∑ j : Fin 2, ∑ nⱼ ∈ Set.Icc (I j).1 (I j).2, (nⱼ⁻¹ : ℚ)) = n } := 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/288background