has given an interesting necessary condition for a polynomial over a finite field of odd characteristic to be irreducible. In Theorem 1 below, I will give a generalization of this result which can also be applied to fields of characteristic 2. It also applies to reducible polynomials and gives the number of irreducible factors mod 2.
No takes yet. Share an insight, caveat, or question.
Richard G. Swan (1962) studied this question.