Power-partible reduction and congruences for Apéry numbers.

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 A k . In particular, we prove that, for any r ∈ ℕ , there exists an integer c ̃ r such that ∑ k = 0 p − 1 (2 k + 1) 2 r + 1 A k ≡ c ̃ r p (mod p 3) holds for any prime p > 3. [ABSTRACT FROM AUTHOR]