Proof of some conjectural hypergeometric supercongruences via curious identities

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:505

Article

Wang, Chen¹  Sun, Zhi-Wei² 

[1] Nanjing Forestry Univ, Dept Appl Math, Nanjing 210037, Peoples R China

[2] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

关键词: Truncated hypergeometric series;    p-adic Gamma function;    Congruences;    Binomial coefficients;   

DOI  :  10.1016/j.jmaa.2021.125575

来源: Elsevier

【 摘 要 】

In this paper, we prove several supercongruences conjectured by Z.-W. Sun ten years ago via certain strange hypergeometric identities. For example, for any prime p > 3, we show that Sigma(p-1)(k=0) ((2k+1) (4k)) ((k) (2k))/48(k) equivalent to 0 (mod p(2)), and Sigma(p-1)(k-0)((2k)(k)) ((3k)(k))/24(k) equivalent to {(p/(p+1)/3(2p+2)/3) ((p-1)/3(2p-2)/3) ((mod p2)) ((mod p2)) if (p equivalent to 2 (mod 3)) (p equivalent to 1 (mod 3)), We also obtain some other results of such types. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free