Skip to content

Erdős problem 786

Start work

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?

Sources

The source's own material, retained exactly.

7 retained statements36c6d0fef71a

Open selected source

FormalConjectures/ErdosProblems/

786.lean

Retained formal statement3 of 7

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?

FormalConjectures/ErdosProblems/786.leanErdos786.erdos_786.parts.i1 lineExact file
True ↔ ∀ ε > 0, ε ≤ 1 → ∃ A δ, 0 ∉ A ∧ 1 - ε < δ ∧ A.HasDensity δ ∧ Erdos786.Set.IsMulCardSet A
OpenStatement only, no proof