Erdős problem 786

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 $r = s$ ?

Sources

The source's own material, retained exactly.

7 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

786.lean

Retained formal statement4 of 7

An example of such a set with density $\frac 1 4$ is given by the integers $\equiv 2\pmod{4}$

FormalConjectures/ErdosProblems/786.leanErdos786.erdos_786.parts.i.example1 lineExact file

1∀ (A : Set ℕ), A = {n | n % 4 = 2} → A.HasDensity (1 / 4) ∧ Erdos786.Set.IsMulCardSet A

TextbookStatement only, no proof