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Every sequence $S$ over $G$ can be written in the form $S=(n_1g)\\cdot\\ldots\\cdot(n_lg)$ where $g\\in G$ and $n_1, \\ldots, n_l\\in[1, \\ord(g)]$, and the index $\\ind(S)$ of $S$ is defined to be the minimum of $(n_1+\\cdots+n_l)/\\ord(g)$ over all possible $g\\in G$ such that $\\langle g \\rangle =G$.\n  A conjecture on the index of length four sequences says that every minimal zero-sum sequence of length 4 over a finite cyclic group $G$ with $\\gcd(|G|, 6)=1$ has index 1. 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