Supercongruences on some binomial sums involving Lucas sequences

被引：5

作者：

Mao, Guo-Shuai ^{[1
]}

Pan, Hao ^{[1
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2017年 / 448卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Pell number; Central binomial coefficient; Congruence; HYPERGEOMETRIC-SERIES; CONGRUENCES; CONJECTURE;

D O I：

10.1016/j.jmaa.2016.10.055

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we confirm several conjectured congruences of Sun concerning the divisibility of binomial sums. For example, with help of a quadratic hypergeometric transformation, we prove that (p-1)Sigma(k=0) [GRAPHICS] (2) P-k/8(k) = 0 (mod p(2)) for any prime p = 7 (mod 8), where P-k is the k-th Pell number. Further, we also propose three new congruences of the same type. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：1061 / 1078

页数：18

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