2012/04/02 by Robert Laterveer, Laterveer, Robert, Myriam Ounaïès +2
Mathematics · Physics and Astronomy · #12D99 #30C15 #30E99 #Advanced Combinatorial Mathematics #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Waves and Solitons #math.CV #msc:12D99 #msc:30C15 #msc:30E99
paper · pdf · doi:10.48550/arxiv.1204.0450
arxiv created 2012/04/02 · openalex publication_date 2012/04/02 · arxiv updated 2012/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Casas-Alvero conjecture states: if a complex univariate polynomial has a common root with each of its derivatives, then it has a unique root. We show that hypothetical counterexamples must have at least 5 different roots. The first case where the conjecture is not known is in degree 12. We study the case of degree 12, and more generally degree p+1, where p is a prime number. While we don't come closing to solving the conjecture in degree 12, we present several further constraints that counterexamples would have to satisfy.