Supercongruences for the (p-1)th Apéry number

2018/03/30 by Ji-Cai Liu, Chen Wang, Liu, Ji-Cai +1
Mathematics · #05A19 #11A07 #11B68 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1803.11442

openalex publication_date 2018/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove two conjectural supercongruences on the (p-1)th Apéry number, which were recently proposed by Z.-H. Sun.

Citations

• Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862--2012)

Related

• Supercongruences involving Apéry-like numbers and Bernoulli numbers
• Supercongruences for polynomial analogs of the Apéry numbers
• Supercongruences arising from a ₇F₆ hypergeometric transformation formula
• A supercongruence involving cubes of Catalan numbers
• Some Numeric Hypergeometric Supercongruences