Source labels openChecked July 26, 2026

Erdős Problem 414

Let $h_1(n) = h(n)$ and $h_k(n) = h(h_{k-1}(n))$ . Is it true, for any $m,n$ , there exist $i$ and $j$ such that $h_i(m) = h_j(n)$ ?

Number theory AMS 11

Mathematical statement

Let $h_1(n) = h(n)$ and $h_k(n) = h(h_{k-1}(n))$ . Is it true, for any $m,n$ , there exist $i$ and $j$ such that $h_i(m) = h_j(n)$ ?

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_414

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_414 : answer(sorry) ↔ ∀ᵉ  (m > 0) (n > 0), ∃ i j, h^[i] m = h^[j] 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/414background