2 problems

Let $\mathbb F_{q^n}/\mathbb F_q$ be a finite field extension. The extension possesses the MM property if it contains an element $a\in\mathbb F_{q^n}$ that is primitive and complet…

Let $p\ge 5$ be a prime and let $n\ge 3$. For $\alpha\in\mathbb{F}_{p^n}$, call $\alpha$ $k$-normal over $\mathbb{F}_p$ if the $\mathbb{F}_p$-vector space spanned by … has dimensio…