Irreducibility criterion for certain trinomials

Abstract

In this article we study the irreducibility of polynomials of the form $x^n+{\epsilon }_1{x}^m+p^k{\epsilon }_2$, $p$ being a prime number. We will show that they are irreducible for $m=1$. We have also provided the cyclotomic factors and reducibility criterion for trinomials of the form $x^n+{\epsilon }_1{x}^m+{\epsilon }_2$, where ${\epsilon }_i\in \{-1,+1\}$. This corrects few of the existing results of W. Ljuggren's on $x^n+{\epsilon }_1{x}^m+{\epsilon }_2$.

6 pages