Corpus.WikipediaBealConjecture.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.
Beal conjecture
formal-conjectures · wikipedia · ams-11
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.
Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).
Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.
Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://en.wikipedia.org/wiki/Beal_conjecture
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Wikipedia/BealConjecture.lean
Local target: Corpus.WikipediaBealConjecture.beal_conjecture
Source SHA-256: 311025f8e363b3f3aeee3b3b3d2354f21ce8bf9263fce95ff00a41697c4fd00b
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.
Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.
Formal targets
Reusable lemmas
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Public discussion
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