Abstract
In recent years, the congruence [Formula: see text] first discovered by the last author has been generalized by either increasing the number of indices and considering the corresponding super congruences, or by considering the alternating version of multiple harmonic sums. In this paper, we prove a family of similar super congruences modulo prime powers [Formula: see text] with the indices summing up to [Formula: see text] where [Formula: see text] is coprime to [Formula: see text], and where all the indices are also coprime to [Formula: see text].
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