关键词: Finite field, primitive polynomial

Abstract:

This paper proves that if qn is large enough, for each element a and primitive element b of Fq, there exists a primitive polynomial of degree n  5 over the finite field Fq having a as the coefficient of xn−1 and b as the constant term. This proves that if qn is large enough, for each element a 2 Fq, there exists a primitive polynomial of degree n  5 over Fq having a as the coefficient of x.

Key words: Finite field, primitive polynomial