The trace of 2-primitive elements of finite fields
Stephen D. Cohen, Giorgos Kapetanakis · Acta Arithmetica · 2019
Let $q$ be a prime power and $n, r$ integers such that $r\,|\, q^n-1$. An element of $\mathbb F _{q^n}$ of multiplicative order $(q^n-1)/r$ is called $r$-primitive. For any odd prime power $q$, we show that there exists a $2$-primitive element of