Proof of a Conjecture of Chowla and Zassenhaus on Permutation Polynomials

Abstract

AbstractThe following conjecture of Chowla and Zassenhaus ( 1968) is proved. If f(x) is an integral polynomial of degree ≧ 2 and p is a sufficiently large prime for which f (considered modulo p) is a permutation polynomial of the finite prime field Fp, then for no integer c with 1 ≦ c < p is f(x) + cx a permutation polynomial of Fp.