# 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.

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