Erdős problem 42
Erdős Problem 42: Let M ≥ 1 and N be sufficiently large in terms of M. Is it true that for every maximal Sidon set A ⊆ {1,…,N} there is another Sidon set B ⊆ {1,…,N} of size M such that (A - A) ∩ (B - B) = {0}?
Sources
FormalConjectures/ErdosProblems/
42.lean
Retained formal statement
Erdős Problem 42: Let M ≥ 1 and N be sufficiently large in terms of M. Is it true that for every maximal Sidon set A ⊆ {1,…,N} there is another Sidon set B ⊆ {1,…,N} of size M such that (A - A) ∩ (B - B) = {0}?
This was proved for all by GPT 5.5 Pro (prompted by Sandhu), see discussion thread for more details.
True ↔ ∀ M ≥ 1, ∀ᶠ (N : ℕ) in Filter.atTop, ∀ (A : Set ℕ), A.IsMaximalSidonSetIn N → ∃ B ⊆ Set.Icc 1 N, IsSidon B ∧ B.ncard = M ∧ (A - A) ∩ (B - B) = {0}