Let $M\ge 1$ and $N$ be sufficiently large in terms of $M$. Is it true that for every Sidon set $A\subset \{1,\dots ,N\}$ there is another Sidon set $B\subset \{1,\dots ,N\}$ of size $M$ such that $(A-A)\cap (B-B)=\{0\}$?

AMS 5 11 · solved (literature)

theorem erdos_42 : answer(True) ↔
    ∀ M ≥ 1, ∀ᶠ N in atTop, ∀ (A : Set ℕ) (_ : IsMaximalSidonSetIn A N),
    ∃ᵉ (B : Set ℕ), B ⊆ Set.Icc 1 N ∧ IsSidon B ∧ B.ncard = M ∧
    ((A - A) ∩ (B - B)) = {0}