1712.07723Dec 20, 201720 pages, a section on self-reciprocal polynomials added, the first moment and second moment (q even) of Fibonacci polynomials computed

Fibonacci self-reciprocal polynomials and Fibonacci permutation polynomials

Neranga Fernando, Mohammad Rashid

Number Theory

arXiv PDF

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 $p>5$

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. 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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