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Erdős problem 329

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Erdős Problem 329. Let A ⊆ ℕ be a Sidon set. How large can lim sup_{N → ∞} |A ∩ {1,…,N}| / N^{1/2} be?

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FormalConjectures/ErdosProblems/

329.lean

Retained formal statement5 of 6

Erdős and Turán [ErTu41] proved the upper bound of 1.

[ErTu41] Erdős, P. and Turán, P., On a problem of Sidon in additive number theory, and on some related problems. J. London Math. Soc. (1941), 212-215.

FormalConjectures/ErdosProblems/329.leanErdos329.erdos_329.variants.turan_19411 lineExact file
∀ (A : Set ℕ), IsSidon A → Erdos329.sidonUpperDensity A ≤ 1
SolvedStatement only, no proof