Amicable numbers
Relatively prime amicable numbers conjecture.* Do there exist amicable numbers with ?
Mathematical statement
Relatively prime amicable numbers conjecture.* Do there exist amicable numbers with ?
All known amicable pairs share a common factor. It is an open question whether a pair of relatively prime amicable numbers can exist. Reference:* Wikipedia
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
relatively_prime_amicable
theorem relatively_prime_amicable : answer(sorry) ↔ ∃ a b : ℕ, IsAmicable a b ∧ a ≠ b ∧ a.Coprime b := 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