Supercongruences on some binomial sums involving Lucas sequences
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- 作者：Guo-Shuai Mao mg1421007@smail.nju.edu.cn ; Hao Pan ; haopan79@zoho.com
- 关键词：Pell number ; Central binomial coefficient ; Congruence
- 刊名：Journal of Mathematical Analysis and Applications
- 出版年：2017
- 出版时间：15 April 2017
- 年：2017
- 卷：448
- 期：2
- 页码：1061-1078
- 全文大小：334 K
- 卷排序：448
文摘
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∑k=0p−1(p−1k)(2kk)2Pk8k≡0(modp2) for any prime p≡7(mod8), where PkPk is the k-th Pell number. Further, we also propose three new congruences of the same type.