6 problems

Gow–McGuire Conjecture 3. For every $\alpha\in\mathbb F_{q^2}\setminus\mathbb F_q$ and every $\mu\in\mathbb F_q^\times$, there exists $\lambda\in\mathbb F_q$ for which…

Gow–McGuire Conjecture 2. For every such irreducible quadratic and every $\mu\in\mathbb F_q^\times$, there exists $\lambda\in\mathbb F_q$ for which $G_{\mu,\lambda}(X)$ is primitiv…

Gow–McGuire Conjecture 1. For every irreducible quadratic $X^2+aX+b\in\mathbb F_q[X]$, there exists $\lambda\in\mathbb F_q$ for which $G_{1,\lambda}(X)$ is primitive over…

Maitra–Gupta–Venkateswarlu conjecture. For every $r=1,\dots,k$ and every pair $1\leq v\ne w\leq t-1$, the exponents satisfy

Let $q$ be a prime and let $\mathbb F_{q^2}$ be the quadratic extension of $\mathbb F_q$. A polynomial of type $P(2,3,q)$ is a primitive polynomial of degree $3$ over…

Let $q$ be prime, let $m,n\geq 2$, and let $\mathbb F_{q^m}$ be the degree-$m$ extension of $\mathbb F_q$. A polynomial $g(X)\in\mathbb F_q[X]$ satisfies $g(0)=0$, and…