*abc* conjecture: Quality
For every positive real number ε, there exist only finitely many triples (a, b, c) of coprime positive integers with a + b = c such that q(a, b, c) > 1 + ε.
Mathematical statement
For every positive real number ε, there exist only finitely many triples (a, b, c) of coprime positive integers with a + b = c such that q(a, b, c) > 1 + ε.
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
abc.variants.quality
theorem abc.variants.quality (ε : ℝ) (hε : 0 < ε) : {(a, b, c) : ℕ × ℕ × ℕ | 0 < a ∧ 0 < b ∧ 0 < c ∧ ({a, b, c} : Set ℕ).Pairwise Nat.Coprime ∧ a + b = c ∧ quality a b c > (1 + ε)}.Finite := 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