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Casas-Alvero conjecture : ウィキペディア英語版 | Casas-Alvero conjecture 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. ==Formal statement== 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.
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