Source labels openChecked July 26, 2026

Erdős Problem 495

Let $\alpha,\beta \in \mathbb{R}$ . Is it true that $\liminf_{n\to \infty} n \| n\alpha \| \| n\beta\| =0$ ? This is also known as the Littlewood conjecture.

Number theory AMS 11

Mathematical statement

Let $\alpha,\beta \in \mathbb{R}$ . Is it true that $\liminf_{n\to \infty} n \| n\alpha \| \| n\beta\| =0$ ? This is also known as the Littlewood conjecture.

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_495

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_495 : answer(sorry) ↔ ∀ α β : ℝ, liminf (fun n : ℕ ↦ (n : ℝ) * distToNearestInt (n * α)  * distToNearestInt (n * β)) atTop = 0 := 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/495background