On polynomials xn − 1 over binary fields whose irreducible factors are binomials and trinomials

Abstract

Let Fq be a finite field with q elements, where q is a power of 2. In this paper we study the positive integers n for which the irreducible factors of the polynomial xn−1 over Fq are all binomials and trinomials. In particular, we completely describe these integers for q=2,4.