Source labels openChecked July 26, 2026

Erdős Problem 409: Iii

What is the density of $n$ which reach any fixed prime under the iteration $n\mapsto\phi(n) + 1$ ?

Number theory AMS 11

Mathematical statement

What is the density of $n$ which reach any fixed prime under the iteration $n\mapsto\phi(n) + 1$ ?

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_409.parts.iii

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_409.parts.iii (p : ℕ) (h : p.Prime) (α : ℝ)    (hα : { n | ∃ i, (φ · + 1)^[i] n = p }.HasDensity α) :    α = answer(sorry) := 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/409background