Finite fields whose members are the sum of a potent and a 4-potent

Stephen D. Cohen, Peter V. Danchev, Tomás Oliveira e Silva

We classify those finite fields ${\mathbb{F}}_q$, for $q$ a power of some fixed prime number, whose members are the sum of an $n$-potent element with $n>1$ and a 4-potent element. It…