
Strong Divisibility, Cyclotomic Polynomials, and Iterated Polynomials.Jeff Sommars
Abstract: In almost all algebra texts, one defines cyclotomic polynomials in reference to the primitive n'th roots of unity. However, as I will show, the property that gcd(x^n1,x^m1)=x^(gcd(m,n))1 is sufficient to define the cyclotomic polynomials uniquely as polynomials in Z[x]. As applications, I will consider implications for cyclotomic polynomials, sequences of the form A^nB^n, polynomial dynamical systems, and rigid divisibility sequences. 