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Erdős problem 786

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Let ϵ>0\epsilon > 0. Is there some set A⊂NA\subset\mathbb{N} of density >1−ϵ> 1 - \epsilon such that a1⋯ar=b1⋯bsa_1\cdots a_r = b_1\cdots b_s with ai,bj∈Aa_i, b_j\in A can only hold when r=sr = s?

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FormalConjectures/ErdosProblems/

786.lean

Retained formal statement6 of 7

Is there some set A⊂{1,...,N}A\subset\{1, ..., N\} of size ≥(1−o(1))N\geq (1 - o(1))N such that a1⋯ar=b1⋯bsa_1\cdots a_r = b_1\cdots b_s with ai,bj∈Aa_i, b_j\in A can only hold when r=sr = s?

FormalConjectures/ErdosProblems/786.leanErdos786.erdos_786.parts.ii4 linesExact file
True ↔  ∃ A f,    ∃ (_ : f =o[Filter.atTop] 1),      ∀ (N : ℕ), A N ⊆ Set.Icc 1 (N + 1) ∧ (1 - f N) * ↑N ≤ ↑(A N).ncard ∧ Erdos786.Set.IsMulCardSet (A N)
OpenStatement only, no proof