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erdos_997.variants.lacunary

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Erdős proved that, if $n_k$ is a lacunary sequence, then the sequence $\{ \alpha n_k\}$ is not well-distributed for almost all $\alpha$.

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Lean 4 Statement 
theorem erdos_997.variants.lacunary (n : ℕ → ℕ) (h : IsLacunary n) :
    ∀ᵐ α, ¬ IsWellDistributed (fun k ↦ Int.fract (α * (n k : ℝ)))
ID: ErdosProblems__997__erdos_997.variants.lacunary
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