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arXiv · 1712.07723

Fibonacci self-reciprocal polynomials and Fibonacci permutation polynomials

Neranga Fernando·Mohammad Rashid
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Abstract

Let $p$ be a prime. In this paper, we give a complete classification of self-reciprocal polynomials arising from Fibonacci polynomials over $\mathbb{Z}$ and $\mathbb{Z}_p$, where $p=2$ and $p>5$. We also present some partial results when $p=3, 5$. We also compute the first and second moments of Fibonacci polynomials $f_{n}(x)$ over finite fields, which give necessary conditions for Fibonacci polynomials to be permutation polynomials over finite fields.

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Neranga Fernando, Mohammad Rashid. 2018-12-29. Fibonacci self-reciprocal polynomials and Fibonacci permutation polynomials. https://arxiv.org/abs/1712.07723

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