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Erdős problem 44

Erdős Problem 44: Let N ≥ 1 and A ⊆ {1,…,N} be a Sidon set. Is it true that, for any ε > 0, there exist M = M(ε) and B ⊆ {N+1,…,M} such that A ∪ B ⊆ {1,…,M} is a Sidon set of size at least (1−ε)M^{1/2}?

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The source's own material, retained exactly.

6 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

44.lean

Retained formal statement4 of 6

The greedy construction gives a Sidon set of size approximately √N.

FormalConjectures/ErdosProblems/44.leanErdos44.greedy_sidon_construction1 lineExact file
∀ (N : ℕ), 1 ≤ N → ∃ A ⊆ Finset.Icc 1 N, IsSidon ↑A ∧ A.card ≥ N.sqrt
TextbookStatement only, no proof