Source labels openChecked July 26, 2026

Erdős Problem 913

Are there infinitely many $n$ such that if $n(n + 1) = \prod_i p_i^{k_i}$ is the factorisation into distinct primes then all exponents $k_i$ are distinct?

Number theory AMS 11

Mathematical statement

Are there infinitely many $n$ such that if

n(n + 1) = \prod_i p_i^{k_i}

is the factorisation into distinct primes then all exponents $k_i$ are distinct?

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_913

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_913 : answer(sorry) ↔    { n | Set.InjOn (n * (n + 1)).factorization (n * (n + 1)).primeFactors }.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/913background