Sobre los números de Sierpiński y Riesel generalizados

In this paper we prove that for any fixed base b >= 2 there exist infinitely many positive integers k such that both kb^n + 1 and kb^n - 1 have at least two distinct prime factors for every positive integer n. In particular, this implies the existence of infinitely many integers that are simultaneously generalized Sierpinski and generalized Riesel numbers. Our approach uses covering systems following the ideas of Erdos and later constructions of Harrington. The argument is then completed using Zsigmondy's theorem on primitive divisors together with properties of multiplicative orders.