The Casas-Alvero conjecture for infinitely many degrees

@article{Bothmer2007TheCC,
  title={The Casas-Alvero conjecture for infinitely many degrees},
  author={H. G. Bothmer and Oliver Labs and J. Schicho and C. V. D. Woestijne},
  journal={Journal of Algebra},
  year={2007},
  volume={316},
  pages={224-230}
}
  • H. G. Bothmer, Oliver Labs, +1 author C. V. D. Woestijne
  • Published 2007
  • Mathematics
  • Journal of Algebra
  • Over a field of characteristic zero, it is clear that a polynomial of the form (X−α)d has a non-trivial common factor with each of its d−1 first derivatives. The converse has been conjectured by Casas-Alvero. Up to now there have only been some computational verifications for small degrees d. In this paper the conjecture is proved in the case where the degree of the polynomial is a power of a prime number, or twice such a power. Moreover, for each positive characteristic p, we give an… CONTINUE READING

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    E-mail address: Labs m @ ath.uni-sb.de, mail O @ liverLabs
      E-mail address: bothmer m @ ath.uni-hannover
        E-mail address: cvdwoest o @ pt.math.tu-graz.ac