Constraints on hypothetical counterexamples to the Casas-Alvero conjecture
Complex Variables
2012-04-03 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1204.0450,
title = {Constraints on hypothetical counterexamples to the Casas-Alvero conjecture},
author = {Robert Laterveer and Myriam Ounaies},
journal= {arXiv preprint arXiv:1204.0450},
year = {2012}
}