All open problems
Source labels openChecked July 26, 2026
Erdős Problem 418: Density
It is open whether the set of non-cototients has positive density.
Mathematical statement
It is open whether the set of non-cototients has positive density.
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_418.variants.density
Complete statement target, proof intentionally absentLean 4
theorem erdos_418.variants.density : answer(sorry) ↔ ∃ (S : Set ℕ) (hS : S.HasPosDensity), S ⊆ { (n - n.totient : ℕ) | n }ᶜ := 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