Biswajit Koley, A. Satyanarayana Reddy: An irreducibility criterion for polynomials over integers, 83-89

Abstract:

In this article, we consider the polynomials of the form $f(x)=a_0+a_1x+a_2x^2+\cdots+a_nx^n\in \Z[x],$ where $\vert a_0\vert=\vert a_1\vert+\dots+\vert a_n\vert$ and $\vert a_0\vert$ is a prime. We show that these polynomials have a cyclotomic factor whenever reducible. As a consequence, we give a simple procedure for checking the irreducibility of trinomials of this form and separability criterion for certain quadrinomials.

Key Words: Irreducible polynomials, cyclotomic polynomials.

2010 Mathematics Subject Classification: Primary 11R09, 12D05, 12D10.