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 $r = s$ ?

Sources

Browse retained paths and inspect the exact material available for this Problem.

7 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

786.lean

Retained formal statement6 of 7

Is there some set $A\subset\{1, ..., N\}$ of size $\geq (1 - o(1))N$ 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.ii4 linesExact file

1True ↔2  ∃ A f,3    ∃ (_ : f =o[Filter.atTop] 1),4      ∀ (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

Sources

Search problems.science