Source labels openChecked July 26, 2026

Erdős Problem 885

Is it true that, for every $k \geq 1$ , there exist integers $N_1 < \dots < N_k$ such that $|\cap_i D(N_i)| \geq k$ ?

Number theory AMS 11

Mathematical statement

Is it true that, for every $k \geq 1$ , there exist integers $N_1 < \dots < N_k$ such that $|\cap_i D(N_i)| \geq k$ ?

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_885

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_885 : answer(sorry) ↔ ∀ k ≥ 1,    ∃ Ns : Finset ℕ,      (∀ n ∈ Ns, 1 ≤ n) ∧      Ns.card = k ∧      (⋂ n ∈ Ns, factorDifferenceSet n).ncard ≥ k := 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/885background