Source labels openChecked July 26, 2026

Erdős Problem 677

Denote by $M(n, k)$ the least common multiple of the finite set $\{n+1, \dotsc, n+k\}$ . Is it true that for all $m \geq n + k$ , we get $M(m, k) \neq M(n, k)$ ?

Number theory AMS 11

Mathematical statement

Denote by $M(n, k)$ the least common multiple of the finite set $\{n+1, \dotsc, n+k\}$ . Is it true that for all $m \geq n + k$ , we get $M(m, k) \neq M(n, k)$ ?

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_677

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_677 :    ∀ (m n k : ℕ), k > 0 → m ≥ n + k → lcmInterval m k ≠ lcmInterval n 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/677background