Source labels openChecked July 26, 2026

Erdős Problem 195

What is the largest $k$ such that in any permutation of $\mathbb{Z}$ there must exist a monotone $k$ -term arithmetic progression $x_1 < \cdots < x_k$ ?

Combinatorics AMS 5

Mathematical statement

What is the largest $k$ such that in any permutation of $\mathbb{Z}$ there must exist a monotone $k$ -term arithmetic progression $x_1 < \cdots < x_k$ ?

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_195

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_195 :    answer(sorry) = sSup {k : ℕ | ∀ f : ℤ ≃ ℤ, HasMonotoneAP f k} := 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/195background