Source labels openChecked July 26, 2026

Beal conjecture

The Beal Conjecture: if we are given positive integers $A, B, C, x, y, z$ such that $x, y, z > 2$ and $A^x + B^y = C^z$ then $A, B, C$ have a common divisor.

Number theory AMS 11

Mathematical statement

The Beal Conjecture: if we are given positive integers $A, B, C, x, y, z$ such that $x, y, z > 2$ and $A^x + B^y = C^z$ then $A, B, C$ have a common divisor.

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

beal_conjecture

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem beal_conjecture : bealConjecture := 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

Pinned Formal Conjectures sourceformalization Wikipediabackground