Ducci-sequences and cyclotomic polynomials

  • Authors:

  • Florian Breuer;Ernest LöTter;Brink Van Der Merwe

  • Affiliations:

  • Department of Mathematics, University of Stellenbosch, Stellenbosch 7600, South Africa;Department of Mathematics, University of Stellenbosch, Stellenbosch 7600, South Africa;Department of Computer Science, University of Stellenbosch, Stellenbosch 7600, South Africa

  • Venue:
  • Finite Fields and Their Applications
  • Year:
  • 2007

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Abstract

We study Ducci-sequences using basic properties of cyclotomic polynomials over F"2. 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 Artin's conjecture on primitive roots.