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Source labels openChecked July 26, 2026

WikipediaNumber theory

Amicable numbers

Relatively prime amicable numbers conjecture.* Do there exist amicable numbers (a,b)(a, b) with gcd(a,b)=1\gcd(a, b) = 1?

Mathematical statement

Relatively prime amicable numbers conjecture.* Do there exist amicable numbers (a,b)(a, b) with gcd(a,b)=1\gcd(a, b) = 1?

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

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem relatively_prime_amicable :    answer(sorry)   a b : , 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