On the reducibility of some polynomials over finite fields with affine polynomials involved
Cao Xi · Scientia Sinica Mathematica · 2010
In this paper,the reducibility of some polynomials over finite fields with affine polynomials involved is investigated.For a given affine trinomial except for xp pt -x-1 over Fp,an explicit factor of it is obtained. The decomposition of g(xp s -ax-b)over Fp has been determined completely.It is also proved that the set of all irreducible polynomials over Fp with the same degree forms a regular graph.In addition,an explicit formula for the number of irreducible factors of g(xq s -x-b)over Fp is presented,where g(x)is an irreducible polynomial over Fp.