4 problems

Cyclotomic-number conjecture. If $\ell\geq 3$, then

Ma–Zha–She's quotient-group conjecture. There is a generator $t\langle -1,2\rangle$ of $\mathbb{Z}_p^{\times}/\langle -1,2\rangle$, for some $t\in\mathbb{Z}_p^{\times}$, such that

Let $p$ be an odd prime, let $H=\langle-1,2\rangle\subset\mathbb{F}_p^{\times}$, let $\ell_0$ be the index parameter used for $H$, and let $g$ be a generator of…

Let $M$ and $w$ be positive integers with $w\geq M$, and let $K(M,L,w)$ denote the maximum number of codewords in an $M$-channel conflict-avoiding code of length $L$ and weight $w$…