2018/10/07 by Ahmadi, Omran, Monsef-Shokri, Kosrov
#11T06 #12E20 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1810.03142
A polynomial f(x) over a field K is called stable if all of its iterates are irreducible over K. In this paper we study the stability of trinomials over finite fields. Specially, we show that if f(x) is a trinomial of even degree over the binary field \mathbbF2, then f(x) is not stable. We prove a similar result for some families of monic trinomials over finite fields of odd characteristic. These results are obtained towards the resolution of a conjecture on the instability of polynomials over finite fields whose degrees are divisible by the characteristic of the underlying field.