Monogenic cyclic polynomials in recurrence sequences
Abstract
Let f(x)∈Z[x] be an Nth degree polynomial that is monic and irreducible over Q. We say that f(x) is monogenic if {1,θ,θ2,…,θN−1} is a basis for the ring of integers of Q(θ), where f(θ)=0. We say that f(x) is cyclic if the Galois group of f(x) over Q is the cyclic group of order N. In this article, we investigate the appearance of monogenic cyclic polynomials in certain polynomial recurrence sequences.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Polynomial and algebraic computation
Publication details
- Journal / source
- Colloquium Mathematicum
- Publication date
- 28 January 2026
- Language
- EN