5 problems

Let $n$ be a positive integer. A three-term arithmetic progression $(a,a+r,a+2r)$ in $\mathbb{Z}/n\mathbb{Z}$, with not all terms equal, is preserved by a permutation…

Index conjecture. If $\gcd(|G|,6)=1$, then every minimal zero-sum sequence $S$ over $G$ of length $4$ satisfies

For a positive integer $n$, let $\mathsf{I}(n)$ denote the maximal index of a minimal zero-sum sequence over a cyclic group of order $n$. Gao's logarithmic conjecture. There is an…

The index conjecture. Every minimal zero-sum sequence $S$ over $G$ of length $|S|=4$ has

Let $\mathbb{Z}_n$ be the finite cyclic group of integers modulo $n$. For a subset $A\subseteq\mathbb{Z}_n$, write $\rho_n(A)$ for the least positive integer $h$ such that every el…