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Polynomials with Irreducible Factors of Specified Degree

Published online by Cambridge University Press:  20 November 2018

Kenneth S. Williams
Kenneth S. Williams*
Affiliation:
Summer Research Institute
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 2 , April 1969 , pp. 221 - 223
Copyright
Copyright © Canadian Mathematical Society 1969