Polynomials with Irreducible Factors of Specified Degree
Kenneth S. Williams · Canadian Mathematical Bulletin · 1969
Let d be a positive integer and let p be a prime > d. Set q = p m , where m ≥ 1, and let I (q, d) denote the number of distinct primary irreducible polynomials of degree d over GF(q). It is a simple deduction from the well-known expression for I(q, d) that (1) where d* is the largest positive integer 1, and d* is 0 if d = 1.