Source labels openChecked July 26, 2026

Erdős Problem 421

Is there a sequence $1 \le d_1 < d_2 < \dots$ with density 1 such that all products $\prod_{u \le i \le v} d_i$ are distinct?

Number theory AMS 11

Mathematical statement

Is there a sequence $1 \le d_1 < d_2 < \dots$ with density 1 such that all products $\prod_{u \le i \le v} d_i$ are distinct?

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_421

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_421 : answer(sorry) ↔    ∃ (d : ℕ → ℕ), StrictMono d ∧ 1 ≤ d 0 ∧ HasDensity (Set.range d) 1 ∧    {(u, v) : ℕ × ℕ | u ≤ v}.InjOn fun (u, v) => ∏ i ∈ Finset.Icc u v, d i := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization erdosproblems.com/421background