Counting Irreducible Polynomials over Finite Fields Using the Inclusion-Exclusion Principle
Sunil K. Chebolu, Ján Mináč · Mathematics Magazine · 2011
SummaryC. 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.