Abstract
Let G be an abelian group and . A Ducci sequence over G is a sequence of n-tuples , where . When G is finite, this sequence is eventually periodic. In this paper, we study Ducci sequences over , where , using properties of cyclotomic polynomials. We first characterize the vanishing sequences (i.e. those for which the cyclic part consists only of 0), as well as the tuples in the cyclic part of a sequence. We then derive an expression for the period of a given Ducci sequence in terms of orders of roots of unity plus one modulo powers of a prime above p in a cyclotomic number field. Lastly, the dependence of the period on t leads us to a connection with Wieferich primes.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
