Permutation properties of the Fibonacci polynomials

Abstract:

The permutation polynomials has wide and important applications in the fields of algebra, combinatorics, number theory, coding theory, cryptography, and so on. In this paper,by calculating the sum of equal powers of the Fibonacci polynomials, we obtain the necessary conditions for determining these Fibonacci polynomials defined on a finite fields is a permutation polynomials, solve the open problem raised by Fernando and Rashid and generalize the existing results.