In this paper, we introduce the power-partible reduction for holonomic (or, P-recursive) sequences and apply it to obtain a series of congruences for Apéry numbers [Formula: see text]. In particular, we prove that, for any [Formula: see text], there exists an integer [Formula: see text] such that [Formula: see text] holds for any prime [Formula: see text].
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Wang et al. (2024) studied this question.
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