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WikipediaNumber theory

Fermat-Catalan conjecture

The Fermat–Catalan conjecture states that the equation am+bn=cka^m + b^n = c^k has only finitely many solutions (a,b,c,m,n,k)(a,b,c,m,n,k) with distinct triplets of values (am,bn,ck)(a^m, b^n, c^k) where a,b,ca, b, c are positive coprime integers and m,n,km, n, k are positive integer...

Number theoryAMS 11

Mathematical statement

The Fermat–Catalan conjecture states that the equation am+bn=cka^m + b^n = c^k has only finitely many solutions (a,b,c,m,n,k)(a,b,c,m,n,k) with distinct triplets of values (am,bn,ck)(a^m, b^n, c^k) where a,b,ca, b, c are positive coprime integers and m,n,km, n, k are positive integers satisfying 1m+1n+1k<1\frac 1 m + \frac 1 n + \frac 1 k < 1.

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

fermat_catalan

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem fermat_catalan : fermatCatalanConjecture := 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 sourceformalizationWikipediabackground