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arXiv · 2606.08024

Monogenity of Fibonacci polynomials and Lucas polynomials

Han Chen·Weizhe Guo·Haojie Hong
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Abstract

We investigate the monogenity of irreducible factors of the Fibonacci polynomials $F_n(x)$ and the Lucas polynomials $L_n(x)$. Our main results show that for every odd positive integer $n$, all irreducible factors of $F_n(x)$ are monogenic, and for every even positive integer $n$, all irreducible factors of $L_n(x)$ are monogenic.

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Han Chen, Weizhe Guo, Haojie Hong. 2026-06-06. Monogenity of Fibonacci polynomials and Lucas polynomials. https://arxiv.org/abs/2606.08024

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