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

Sunil K. Chebolu and Ján Miná?
Mathematics Magazine
Vol. 84, No. 5 (December 2011), pp. 369-371
DOI: 10.4169/math.mag.84.5.369
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.84.5.369
Page Count: 3
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Counting Irreducible Polynomials over Finite Fields Using the Inclusion-Exclusion Principle
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Abstract

Summary C. F. Gauss discovered a beautiful formula for the number of irreducible polynomials of a given degree over a finite field. Using just very basic knowledge of finite fields and the inclusion-exclusion formula, we show how one can see the shape of this formula and its proof almost instantly.

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