Counting irreducible polynomials over finite fields using the inclusion-exclusion principle
classification
🧮 math.HO
math.NT
keywords
formulafieldfiniteirreduciblepolynomialsassumingbeautifulcounting
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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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