1 January 2019
REVISTA MATEMATICA IBEROAMERICANA
© European Mathematical Society For a set S of quadratic polynomials over a finite field, let C be the (infinite) set of arbitrary compositions of elements in S. In this paper we show that there are examples with arbitrarily large S such that every polynomial in C is irreducible. As a second result, when #S > 1, we give an algorithm to determine whether all the elements in C are irreducible, using only O(#S(log q)3q1/2) operations.
Submitted to ORA: