2 problems

Let $K$ be a $2$-adic local field and let $0\leq t\leq s\leq e=v_K(2)$. Let $C_1\subseteq C_2$ be orders in a cubic $K$-algebra $R$ with $C_2/C_1\cong\mathcal{O}_K/\pi^{s-t}$ cycli…

Let $n$ be a positive odd integer. Let $f$ be a polynomial of degree $n$ with no multiple roots and only one real root. A $2\times n\times n$ box is a pair $(A,B)$ of $n\times n$ i…