3 problems

Let $\mathbb{F}_{q}$ be a finite field with $q=p^{e}$ elements, and fix a positive integer $M$. Large-factor-degree conjecture. There is a constant $C$ such that for every integer…

Let $a\in\mathbb{Q}^{*}$ and let … where $n>m>k$. Multiple-factor conjecture. If $f_{n,m,k}(a,x)$ has multiple factors, then $a=1$ and … for some $d\geq 1$ and odd integers…

Finiteness conjecture. There are only finitely many triples of exponents $n,m,k$ and integers $a$ such that