PapersField theory and polynomials
Casas-Alvero Conjecture
The Casas-Alvero conjecture states that in characteristic zero, if a monic polynomial P has the Casas-Alvero property, then P = (X - α)ᵈ for some α.
Mathematical statement
The Casas-Alvero conjecture states that in characteristic zero, if a monic polynomial P
has the Casas-Alvero property, then P = (X - α)ᵈ for some α.
Statement source: Papers statement material
Statement terms: Source-specific
Source-specific terms. Therefore does not assert reuse rights beyond attributed display.
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
casas_alvero_conjecture
theorem casas_alvero_conjecture (hP' : HasCasasAlveroProp P) : ∃ α : K, P = (X - C α) ^ P.natDegree := 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