Supercongruences for sums involving Domb numbers

被引：4

作者：

Liu, Ji-Cai ^{[1
]}

机构：

[1] Wenzhou Univ, Dept Math, Wenzhou 325035, Peoples R China

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2021年 / 169卷

基金：

中国国家自然科学基金;

关键词：

Supercongruences; Domb numbers; Franel numbers; Euler numbers; CONGRUENCES; TRANSFORMATIONS; CONJECTURES; PROOF;

D O I：

10.1016/j.bulsci.2021.102992

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove some supercongruence and divisibility results on sums involving Domb numbers, which confirm four conjectures of Z.-W. Sun and Z.-H. Sun. For instance, by using a transformation formula due to Chan and Zudilin, we show that for any prime p >= 5, Sigma(k = 0) (p 1) 3k + 1/(-32)(k) Domb (k) (-1) p - 1/2 p + p(3) Ep - 3 (mod p(4)) which is regarded as a p-adic analogue of the interesting formula for 1/pi to Rogers: Sigma(infinity)(k = 0) 3k + 1/(-32)(k) Domb (k) = 2/pi. Here Domb(n) and E-n the famous Domb numbers and Euler numbers. (C) 2021 Elsevier Masson SAS. All rights reserved.

引用

页数：13

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