On the degrees of which there exist no self-reciprocal binary irreducible pentanomials

Abstract

Omran Ahmadi proved that if a number n is divisible by 12, there is no self-reciprocal irreducible pentanomial of degree n over F2. We found new sets of numbers holding this property, including the numbers n = 2 • 3^k>k > 1. As the degrees are all integers, a new observation on the degrees of which there exist no self-reciprocal binary irreducible pentanomials from the Ulam spiral is also presented. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.