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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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Problem row
sha256:d1f856b92ef11ad53539bbca82c41e29aeb22ef507817e50552e827c2eb53797
Metadata
sha256:fc7c25be4c322a5b6b1926ded51768759d0602818677bb353de987aca438ca04
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:ca696c0edde9f6e5853c9afb77dc7b45c365ded25e0acd5ae6e0ad8ec3543b00
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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