New polynomials producing absolute pseudoprimes with any number of prime factors

Abstract

In this paper, we introduce a certain method to construct polynomials producing many absolute pseudoprimes. By this method, we give new polynomials producing absolute pseudoprimes with any fixed number of prime factors which can be viewed as a generalization of Chernick's result. By the similar method, we give another type of polynomials producing many absolute pseudoprimes. As concrete examples, we tabulate the counts of such numbers of our forms.