Solitary Numbers
Existence of an infinite club.* A club is an abundancy equivalence class, i.e. the set of all positive integers friendly with a given . It is unknown whether any club is infinite.
Mathematical statement
Existence of an infinite club.* A club is an abundancy equivalence class, i.e. the set of all positive integers friendly with a given . It is unknown whether any club is infinite.
Statement source: Wikipedia statement material
Statement terms: CC-BY-SA-4.0
Attributed source material. Reuse must follow the linked attribution and share-alike terms.
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
infinite_club_exists
theorem infinite_club_exists : answer(sorry) ↔ ∃ n, 0 < n ∧ {m : ℕ | Friendly m n}.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