Counting irreducible polynomials over finite fields using the inclusionexclusion 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 exclusioninclusion formula, we show how one see the shape of this formula and its proof instantly.
 Publication:

arXiv eprints
 Pub Date:
 January 2010
 arXiv:
 arXiv:1001.0409
 Bibcode:
 2010arXiv1001.0409C
 Keywords:

 Mathematics  History and Overview;
 Mathematics  Number Theory
 EPrint:
 3 pages, final version, to appear in Mathematics Magazine