The Casas-Alvero conjecture predicts that every univariate polynomial over a
field of characteristic zero having a common factor with each of its
derivatives Hiβ(f) is a power of a linear polynomial. One approach to proving
the conjecture is to first prove it for polynomials of some small degree d,
compile a list of bad primes for that degree (namely, those primes p for
which the conjecture fails in degree d and characteristic p) and then
deduce the conjecture for all degrees of the form dpβ,
ββN, where p is a good prime for d. In this paper we
calculate certain distinguished monomials appearing in the resultant
R(f,Hiβ(f)) and obtain a (non-exhaustive) list of bad primes for every degree
dβNβ{0}