An irreducible class of polynomials over integers

Biswajit Koley; A. Satyanarayana Reddy

paper

An irreducible class of polynomials over integers

arXiv:2004.00233

Abstract

In this article, we consider polynomials of the form $f (x) = a_{0} + a_{n_{1}} x^{n_{1}} + a_{n_{2}} x^{n_{2}} + \dots + a_{n_{r}} x^{n_{r}} \in Z [x],$ where $∣ a_{0} ∣ \geq ∣ a_{n_{1}} ∣ + \dots + ∣ a_{n_{r}} ∣,$ $∣ a_{0} ∣$ is a prime power and $∣ a_{0} ∣ ∤ ∣ a_{n_{1}} a_{n_{r}} ∣$ . We will show that under the strict inequality these polynomials are irreducible for certain values of $n_{1}$ . In the case of equality, apart from its cyclotomic factors, they have exactly one irreducible non-reciprocal factor.

12 pages