Erdős problem 786 · problems.science

Let $\epsilon > 0$ . Is there some set $A\subset\mathbb{N}$ of density $> 1 - \epsilon$ 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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FormalConjectures/ErdosProblems/

786.lean

Retained formal statement3 of 7

Let $\epsilon > 0$ . Is there some set $A\subset\mathbb{N}$ of density $> 1 - \epsilon$ such that $a_1\cdots a_r = b_1\cdots b_s$ with $a_i, b_j\in A$ can only hold when $r = s$ ?

FormalConjectures/ErdosProblems/786.leanErdos786.erdos_786.parts.i1 lineExact file

1True ↔ ∀ ε > 0, ε ≤ 1 → ∃ A δ, 0 ∉ A ∧ 1 - ε < δ ∧ A.HasDensity δ ∧ Erdos786.Set.IsMulCardSet A

OpenStatement only, no proof

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