Matches in DBpedia 2014 for { ?s ?p In mathematics, the Casas-Alvero conjecture is an open problem about polynomials which have factors in common with their derivatives, proposed by Eduardo Casas-Alvero in 2001.Let f be a polynomial of degree d defined over a field K of characteristic zero. If f has a factor in common with each of its derivatives f(i), i = 1, ..., d − 1 then the conjecture predicts that f must be a power of a linear factor. The conjecture is clearly false over a field of characteristic p: any inseparable polynomial f(Xp) satisfies the condition since all derivatives are zero. Another, separable, counter-example is Xp+1 − XpThe conjecture is known to hold in characteristic zero for degrees which are prime power or twice a prime power: hence for all d up to 11. It has recently been established for d = 12.. }
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- Casas-Alvero_conjecture abstract "In mathematics, the Casas-Alvero conjecture is an open problem about polynomials which have factors in common with their derivatives, proposed by Eduardo Casas-Alvero in 2001.Let f be a polynomial of degree d defined over a field K of characteristic zero. If f has a factor in common with each of its derivatives f(i), i = 1, ..., d − 1 then the conjecture predicts that f must be a power of a linear factor. The conjecture is clearly false over a field of characteristic p: any inseparable polynomial f(Xp) satisfies the condition since all derivatives are zero. Another, separable, counter-example is Xp+1 − XpThe conjecture is known to hold in characteristic zero for degrees which are prime power or twice a prime power: hence for all d up to 11. It has recently been established for d = 12.".