Power-Partible Reduction and Congruences for Apéry Numbers

2023/01/05 by Wang, Rong-Hua, Zhong, Michael X. X. · 1 citation
#05A10 #11A07 #33F10 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2301.01985

Abstract

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(2k+1)^2r+1A_k≡ c_r p \pmod p³ holds for any prime p>3.

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