Abstract
The Index Conjecture in zero-sum theory states that when n is coprime to 6 and k equals 4, every minimal zero-sum sequence of length k modulo n has index 1. While other values of (k,n) have been studied thoroughly in the last 30 years, it is only recently that the conjecture has been proven for n>1020. In this paper, we prove that said upper bound can be reduced to 4.6⋅1013, and lower under certain coprimality conditions. Further, we verify the conjecture for n<1.8⋅106 through the application of High Performance Computing (HPC).
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