Lethbridge Number Theory and Combinatorics Seminar: Adam Felix

Let $a \in \mathbb{Z} \setminus \{0,\pm 1\}$, and let $f_{a}(p)$ denote the order of $a$ modulo $p$, where $p \nmid a$ is prime.  There are many results that suggest $p - 1$ and $f_{a}(p)$ are close.  For example, Artin's conjecture and Hooley's subsequent proof upon the Generalized Riemann Hypothesis.  We will examine questions related to the relationship between $p - 1$ and $f_{a}(p)$.