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Erdős problem 495

Let α,β∈R\alpha,\beta \in \mathbb{R}. Is it true thatlim inf⁡n→∞n∥nα∥∥nβ∥=0\liminf_{n\to \infty} n \| n\alpha \| \| n\beta\| =0? This is also known as the Littlewood conjecture.

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FormalConjectures/ErdosProblems/

495.lean

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Let α,β∈R\alpha,\beta \in \mathbb{R}. Is it true thatlim inf⁡n→∞n∥nα∥∥nβ∥=0\liminf_{n\to \infty} n \| n\alpha \| \| n\beta\| =0? This is also known as the Littlewood conjecture.

FormalConjectures/ErdosProblems/495.leanErdos495.erdos_4951 lineExact file
True ↔ ∀ (α β : ℝ), Filter.liminf (fun n => ↑n * distToNearestInt (↑n * α) * distToNearestInt (↑n * β)) Filter.atTop = 0
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