Coverings of the Integers Associated with an Irreducibility Theorem of A. Schinzel
Michael A. Filaseta · 2024
The purpose of this paper is to give a partially expository account of results related to coverings of the integers (defined below) while at the same time making some new observations concerning a related polynomial problem. The polynomial problem we will consider is to determine whether for a given positive integer d there exists an f ( x ) ∈ ℤ + [ x ] such that f ( x ) x n + d is reducible over the rationals for every non-negative integer n . We begin with some background material.