Counting irreducible polynomials over finite fields using the inclusion-exclusion principle

Abstract

C. F. Gauss discovered a beautiful formula for the number of irreducible polynomials of a given degree over a finite field. Assuming just a few elementary facts in field theory and the exclusion-inclusion formula, we show how one see the shape of this formula and its proof instantly.

arXiv comment3 pages, final version, to appear in Mathematics Magazine