Source labels openChecked July 26, 2026

Erdős Problem 348

For what values of $0 \leq m < n$ is there a complete sequence $A = \{a_1 \leq a_2 \leq \cdots\}$ of integers such that 1. $A$ remains complete after removing any $m$ elements, but 2. $A$ is not complete after removing any $n$ elements.

Number theory AMS 11

Mathematical statement

For what values of $0 \leq m < n$ is there a complete sequence $A = \{a_1 \leq a_2 \leq \cdots\}$ of integers such that

$A$ remains complete after removing any $m$ elements, but
$A$ is not complete after removing any $n$ elements.

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_348

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_348 :    { (m, n) | (m) (n) (_ : m < n) (a : ℕ → ℕ) (_ : Monotone a)      (_ : ∀ s, s.card = m → IsAddComplete (Set.range (Function.updateFinset a s 0)))        (_ : ∀ t, t.card = n → ¬IsAddComplete (Set.range (Function.updateFinset a t 0))) } =    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/348background