5 problems

Let $p\geq 5$ be prime and let $n\geq 3$ be an integer. An element of $\mathbb{F}_{p^n}$ is $k$-normal over $\mathbb{F}_p$ when the greatest common divisor of its associated polyno…

Conjecture. For every such $q$, $(q,7)\in A$.

Let $t$ be a positive integer. A pair $(\alpha,\alpha^{-1})$ is a pair of primitive $1$-normal elements in $\mathbb{F}_{q^n}$ over $\mathbb{F}_q$ when both elements are primitive a…

Let $p$ be a prime, let $n=p$, let $a$ be a primitive element of $\mathbb{F}_p$, and let $\alpha\in\mathbb{F}_{p^p}$ be a root of the irreducible polynomial … Such an $\alpha$ is…

Mullen–Anderson conjecture. For each $k=0,1$ and $a=1,2$, there exists a $k$-normal element $\alpha\in\mathbb{F}_{p^n}$ with multiplicative order