Supercongruences on some binomial sums involving Lucas sequences

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:448

Article

Mao, Guo-Shuai¹  Pan, Hao¹ 

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

关键词: Pell number;    Central binomial coefficient;    Congruence;   

DOI  :  10.1016/j.jmaa.2016.10.055

来源: Elsevier

【 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.

【 授权许可】

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