2 problems

Let $1\leq m<n$, let $a,b,c$ be integers, and define … Assume that $\gcd(n,mb)=1$ and that $a$ is prime. Jones's monogenicity conjecture. The polynomial $g(x)$ is monogenic if and…

Let $a,b\in\mathbb{Z}$. Let $p$ and $q$ be odd primes with $p\equiv -1 \\(\operatorname{mod}~p)$. Define … Suppose that $\mathcal K(|ap|)=\mathcal K(|b^q+a|)$, where…