Let d be a positive integer and let p be a prime > d. Set q = pm, 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 < d which divides d if d > 1, and d* is 0 if d = 1.