All open problems
Source labels openChecked July 26, 2026

Erdős ProblemsNumber theory

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

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_418.variants.density :    answer(sorry)   (S : Set ) (hS : S.HasPosDensity), S  { (n - n.totient : ) | 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