Power-partible reduction and congruences for Apéry numbers
Ronghua Wang, Michael X. X. Zhong · International Journal of Number Theory · 2024
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].