3 problems

Let $q$ be a prime power and let $\textbf{F}_{q^n}$ be a finite field. Let $g\in\textbf{F}_{q^n}$ satisfy the conditions in Theorem, and suppose that $n\geq\log q$. Large-order con…

Let $n=am+1$, where $a$ and $m$ are positive integers, and let $p$ be the least prime divisor of $m$. Primality conjecture. If $a<p$ and $m\mid\phi(n)$, then $n$ is prime. This con…

Determinism conjecture. If