English

On the generalized Fibonacci sequence of polynomials over finite fields

Number Theory 2023-03-31 v1

Abstract

In this paper, as an analogue of the integer case, we study detailedly the period and the rank of the generalized Fibonacci sequence of polynomials over a finite field modulo an arbitrary polynomial. We establish some formulas to compute them, and we also obtain some properties about the quotient of the period and the rank. We find that the polynomial case is much more complicated than the integer case.

Keywords

Cite

@article{arxiv.2303.17525,
  title  = {On the generalized Fibonacci sequence of polynomials over finite fields},
  author = {Zekai Chen and Min Sha and Chen Wei},
  journal= {arXiv preprint arXiv:2303.17525},
  year   = {2023}
}

Comments

33 pages

R2 v1 2026-06-28T09:41:40.728Z