Counting Irreducible Polynomials over Finite Fields Using the Inclusion-Exclusion Principle

@article{Chebolu2010CountingIP,
  title={Counting Irreducible Polynomials over Finite Fields Using the Inclusion-Exclusion Principle},
  author={Sunil K. Chebolu and J. Min{\'a}c},
  journal={Mathematics Magazine},
  year={2010},
  volume={84},
  pages={369 - 371}
}
Summary C. F. Gauss discovered a beautiful formula for the number of irreducible polynomials of a given degree over a finite field. Using just very basic knowledge of finite fields and the inclusion-exclusion formula, we show how one can see the shape of this formula and its proof almost instantly. 
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Using just very basic knowledge of finite fields and the inclusion-exclusion formula, we show how one can see the shape of this formula and its proof almost instantly