In mathematics, the Dickson polynomials (or Brewer polynomials), denoted Dn(x,α), form a polynomial sequence introduced by L. E. Dickson (1897) and rediscovered by Brewer (1961) in his study of Brewer sums.
Over the complex numbers, Dickson polynomials are essentially equivalent to Chebyshev polynomials with a change of variable, and in fact Dickson polynomials are sometimes called Chebyshev polynomials. Dickson polynomials are mainly studied over finite fields, when they are not equivalent to Chebyshev polynomials. One of the main reasons for interest in them is that for fixed α, they give many examples of permutation polynomials: polynomials acting as permutations of finite fields.
Other articles related to "dickson polynomial, polynomial, dickson polynomials, polynomials":
... A permutation polynomial (for a given finite field) is one that acts as a permutation of the elements of the finite field ... The Dickson polynomial Dn(x,α) (considered as a function of x with α fixed) is a permutation polynomial for the field with q elements whenever n is coprime to q2−1 ... Fried (1970) proved that any integral polynomial that is a permutation polynomial for infinitely many prime fields is a composition of Dickson polynomials and linear polynomials (wit ...