On the Casas-Alvero’ s Conjecture

Abstract As we all know, every derivation of a polynomial that is a nth degree of another polynomial has a common factor with this polynomial. Then, Eduardo Casas-Alvero came up with a conjecture that think opposite with the axiom we just talked before. That is to proof this polynomial is a nth degr...

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Bibliographic Details
Published inJournal of physics. Conference series Vol. 1955; no. 1; pp. 12020 - 12030
Main Author Su, Jiaxuan
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.06.2021
Subjects
Derivation
Physics
Polynomials
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Summary:Abstract As we all know, every derivation of a polynomial that is a nth degree of another polynomial has a common factor with this polynomial. Then, Eduardo Casas-Alvero came up with a conjecture that think opposite with the axiom we just talked before. That is to proof this polynomial is a nth degree of another polynomial if every derivation of this polynomial has a common factor with this polynomial. We are going to use different method to attack this conjecture and prove it when n is small.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1955/1/012020