Amicable numbers
Amicable numbers with opposite parity conjecture.* Do there exist amicable numbers where one is even and the other is odd?
Mathematical statement
Amicable numbers with opposite parity conjecture.* Do there exist amicable numbers where one is even and the other is odd?
All known amicable pairs are either both even or both odd. It is widely believed that mixed-parity amicable pairs do not exist, but this remains open. Reference:* Wikipedia
Statement source: Wikipedia statement material
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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
opposite_parity_amicable
theorem opposite_parity_amicable : answer(sorry) ↔ ∃ a b : ℕ, IsAmicable a b ∧ (Even a ↔ Odd 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