On the properties of fibotomic polynomials
Number Theory
2025-06-24 v1
Abstract
Define the -th fibotomic polynomial to be the product of the monic irredicible factors of the -th Fibonacci polynomial which are not factors of any Fibonacci polynomial of smaller degree. In this paper, we prove a number of properties of the fibotomic polynomials. This includes determining the discriminant of the fibotomic polynomials and the resultant of pairs of fibotomic polynomials. Furthermore, we completely determine the factorization form of the fibotomic polynomials in prime fields. Results are also generalized for the bivariate homogenous fibotomic polynomials.
Keywords
Cite
@article{arxiv.2009.03345,
title = {On the properties of fibotomic polynomials},
author = {Cameron Byer and Tyler Dvorachek and Emily Eckard and Joshua Harrington and Lindsey Wise and Tony W. H. Wong},
journal= {arXiv preprint arXiv:2009.03345},
year = {2025}
}