Solution to the index conjecture in zero-sum theory

A problem in zero-sum theory is to determine all pairs $(k,n)$ for which every minimal zero-sum sequence of length $k$ modulo $n$ has index $1$. While all other cases have been solved more than a decade ago, the case when $k$ equals $4$ and $n$ is coprime to $6$ remains open. Precisely, The Index Conjecture in this subject states that if $n$ is coprime to $6$ then every minimal zero-sum sequence of length $4$ modulo $n$ has index $1$. In this paper, we prove an equivalent version of this conjecture for all $n>N$ for some absolute constant $N$.