Source labels openChecked July 26, 2026

Erdős Problem 1146

Is $B=\{2^m3^n : m,n\geq 0\}$ an essential component?

Mathematical statement

Is $B=\{2^m3^n : m,n\geq 0\}$ an essential component?

In [Ru99] Ruzsa states "The simplest set with a chance to be an essential component is the collection of numbers in the form $2^m3^n$ and Erdős often asked whether it is an essential component or not; I do not even have a plausible guess."

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_1146

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_1146 :    answer(sorry) ↔ IsEssentialComponent { k | ∃ m n : ℕ, k = 2 ^ m * 3 ^ n } := 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/1146background