WOLSTENHOLME TYPE THEOREM FOR MULTIPLE HARMONIC SUMS

In this paper, we will study the p-divisibility of multiple harmonic sums (MHS) which are partial sums of multiple zeta value series. In particular, we provide some generalizations of the classical Wolstenholme's Theorem to both homogeneous and non-homogeneous sums. We make a few conjectures at the end of the paper and provide some very convincing evidence.