We prove a generalization of the Newton Identities for entire functions, which give a relation between the Taylor coefficients and sums of powers of reciprocals of the zeros of an entire function. We apply these identities to a number of special functions, yielding some interesting recursion relations.
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… (More)