Monogenity of the irreducible factors of $(k,t)$-Fibonacci and $(k,t)$-Lucas polynomials

Michail Karatarakis; Sumandeep Kaur

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arXiv · 2609.38844

Monogenity of the irreducible factors of $(k,t)$-Fibonacci and $(k,t)$-Lucas polynomials

Michail Karatarakis·Sumandeep Kaur

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Abstract

In this article, we study the monogenity of the number field generated by a root of an irreducible factor of the generalized $(k,t)$-Fibonacci and $(k,t)$-Lucas polynomial sequence. We use Dickson polynomials and their connection with cyclotomic fields to prove our main results. As special cases, we recover the monogenity results for the classical Fibonacci and Lucas polynomials and obtain corresponding monogenity results for Chebyshev polynomials of the first and second kinds.

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Michail Karatarakis, Sumandeep Kaur. 2026-09-30. Monogenity of the irreducible factors of $(k,t)$-Fibonacci and $(k,t)$-Lucas polynomials. https://arxiv.org/abs/2609.38844

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