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

摘要

Omran Ahmadi proved that if a number n is divisible by 12, there is no self-reciprocal irreducible pentanomial of degree n over F-2. 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.