The third-order factorable core of polynomials over finite fields
Javier Gomez-Calderon · Proceedings of the Japan Academy Series A Mathematical Sciences · 1998
Let Fq denote the finite field of order q and characteristic p.Forf(x) in Fq[x ], let f* (x, y) denote the substitution polynomial f(x)-f(y).In this paper we show that if d d-2 d-3 f(x) x + aa_zx + aa_ax + a t-alX a t-ao Fq[x] (ae_zae_ =/: O) has degree d prime to q and f*(x, y) has at least one cubic irreducible factor, then Fq[x] where r denotes the number of irreducible cubic factors of f*(x, y) of the form xTy + Ax+By+ C.