Counting Irreducible Polynomials over Finite Fields Using the Inclusion-Exclusion Principle

by Sunil K. Chebolu (Illinois State University) and Ján Mináč (University of Western Ontario)

This article originally appeared in:
Mathematics Magazine
December, 2011

Subject classification(s): Algebra and Number Theory | Abstract Algebra | Fields
Applicable Course(s): 4.2 Mod Algebra I & II

Using just very basic knowledge of finite fields and the inclusion-exclusion formula, the authors show how one can see the shape of Gauss` formula for the number of irreducible polynomials of a given degree over a finite field .

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