THE COEFFICIENTS OF PRIMITIVE POLYNOMIAL OVER FINITE FIELD
Wenbao Han · Chinese Annals of Mathematics,series A · 2004
Let f(x) = xn + a1xn-1+…+an-1x + an be a polynomial over Fq, where Fq denotes the finite field of q elements, q an odd prime power. When n ≥ 7, Han has stated that there exist a primitive polynomial of degree n with a1, a2 prescribed. In this paper, the authors discuss the remaining cases when n = 5,6. By making use of two kinds of exponential sums and Cohen's Sieve, the authors improve the lower bound of primitive solutions and prove that there exists a primitive polynomial of degree n = 5,6 with a1,a2 prescribed.