Is there some set $A\subset\{1, ..., N\}$ of size $\geq (1 - o(1))N$ such that
$a_1\cdots a_r = b_1\cdots b_s$ with $a_i, b_j\in A$ can only hold when
$r = s$?
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theorem erdos_786.parts.ii : answer(sorry) ↔
∃ (A : ℕ → Set ℕ) (f : ℕ → ℝ) (_ : f =o[atTop] (1 : ℕ → ℝ)),
∀ N, A N ⊆ Set.Icc 1 (N + 1) ∧ (1 - f N) * N ≤ (A N).ncard ∧ (A N).IsMulCardSet
