Source labels openChecked July 26, 2026

Erdős Problem 730

Are there infinitely many pairs of integers $n < m$ such that $\binom{2n}{n}$ and $\binom{2m}{m}$ have the same set of prime divisors?

Number theory AMS 11

Mathematical statement

Are there infinitely many pairs of integers $n < m$ such that $\binom{2n}{n}$ and $\binom{2m}{m}$ have the same set of prime divisors?

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_730

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_730 : answer(sorry) ↔ S.Infinite := 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/730background A129515background