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Erdős problem 158

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Let A be an infinite B₂[2] set. Must liminf |A ∩ {1, ..., N}| * N ^ (- 1 / 2) = 0?

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4 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

158.lean

Retained formal statement4 of 4

Let A be an infinite Sidon set. Then liminf |A ∩ {1, ..., N}| * N ^ (- 1 / 2) * (log N) ^ (1 / 2) < ∞. This is proved in [ESS94].

FormalConjectures/ErdosProblems/158.leanErdos158.erdos_158.variants.isSidon'6 linesExact file
∀ {A : Set ℕ},  A.Infinite →    IsSidon A →      Filter.liminf (fun N => ENNReal.ofReal (↑(A ∩ Set.Iio N).ncard * ↑N ^ (-1 / 2) * Real.log ↑N ^ (1 / 2)))          Filter.atTop <        ⊤
SolvedStatement only, no proof