All open problems
Source labels openChecked July 26, 2026
Erdős Problem 940: Large Integers
It is not known if all large integers are the sum of at most -many -powerful numbers.
Mathematical statement
It is not known if all large integers are the sum of at most -many -powerful numbers.
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_940.variants.large_integers
Complete statement target, proof intentionally absentLean 4
theorem erdos_940.variants.large_integers : answer(sorry) ↔ ∀ r ≥ 2, (∀ᶠ x in atTop, ∃ (S : Multiset ℕ), S.card ≤ r ∧ (∀ s ∈ S, r.Full s) ∧ x = S.sum) := 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