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

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

2010-01-03

arxiv.org/abs/1001.0409v6

Mathematics

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3 pages, final version, to appear in Mathematics Magazine

Scientific paper

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.

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