The Casas-Alvero conjecture is a problem in mathematics about polynomials which have factors in common with their derivatives, proposed by Eduardo Casas-Alvero in 2001. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementIf a polynomial f has a factor in common with each of its derivatives of order 1 to d-1, then f must be a power of a linear polynomial. 1 Proposed Year Progress Toward ResolutionKnown to hold in characteristic zero for degrees of the form p^k or 2p^k, where p is prime and k is a positive integer. 1 Classification
Resolution Status Prize Status
Prize Status (category) Connections
In Branch
Source Casas-Alvero Conjecture (Wikipedia)
Sources
1. Casas-Alvero Conjecture (Wikipedia)
Wikimedia FoundationLead section
proposed by Eduardo Casas-Alvero in 2001
Formal statement
then the conjecture predicts that f must be a power of a linear polynomial.
Special cases
The conjecture is known to hold in characteristic zero for degrees of the form
In Branch: Algebra, Lead
In mathematics, the Casas-Alvero conjecture is a problem about polynomials which have factors in common with their derivatives, proposed by Eduardo Casas-Alvero in 2001.
View the Source Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.