Ducci-sequences and cyclotomic polynomials

We study Ducci-sequences using basic properties of cyclotomic polynomials over . We determine the period of a given Ducci-sequence in terms of the order of a polynomial, and in terms of the multiplicative orders of certain elements in finite fields. We also compute some examples and study links between Ducci-sequences, primitive polynomials and Artinʹs conjecture on primitive roots.