Source labels openChecked July 26, 2026

Erdős Problem 826

Are there infinitely many $n$ such that, for all $k\geq 1$ $\tau(n + k) \ll k?$

Mathematical statement

Are there infinitely many $n$ such that, for all $k\geq 1$

\tau(n + k) \ll 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_826

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_826 : answer(sorry) ↔    ∃ C > (0 : ℝ), { n | ∀ k ≥ 1, σ 0 (n + k) ≤ C * k }.Infinite := 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/826background