# Journal of the Ramanujan Mathematical Society

Volume 37, Issue 4, December 2022  pp. 319–330.

An irreducible class of polynomials over integers

Authors:  Biswajit Koley and A. Satyanarayana Reddy
Author institution: Department of Mathematics, Shiv Nadar University, Uttar Pradesh 201 314, India.

Summary:  In this article, we consider polynomials of the form f(x) = p{u}ε +a{n1}x{n1} + a{n2}x{n2} +···+a{nr} x{nr} ∈ Z[x], where pu ≥ |a{n1}| +··· + |a{nr}|, ε = ± 1, and p is a prime number, p ∤ |a{n1}a{nr}|. 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.