Counting irreducible polynomials over finite fields using the inclusion-exclusion principle
History and Overview
2011-03-17 v6 Number Theory
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.
Cite
@article{arxiv.1001.0409,
title = {Counting irreducible polynomials over finite fields using the inclusion-exclusion principle},
author = {Sunil K. Chebolu and Jan Minac},
journal= {arXiv preprint arXiv:1001.0409},
year = {2011}
}
Comments
3 pages, final version, to appear in Mathematics Magazine