ON PERMUTATION BINOMIALS

摘要

Let F-q be the finite field of characteristic p containing q = p(r) elements. Let f(x) = ax(n) + x(m) be a binomial with coefficients in F-q and d = gcd (n - m, q - 1). In this paper, we prove that there does not exist any permutation binomial such that d satisfies certain congruence conditions, and we do some computations to list all non permutation binomials for n - m = 3 and q <= 100.