On some congruences of certain binomial sums

被引：17
|
作者：
Chen, Yungui [1 ]
Xie, Xiaoyan [1 ]
He, Bing [2 ]
机构：
[1] Inner Mongolia Univ Technol, Coll Management, 49 Aimin St, Hohhot 010051, Inner Mongolia, Peoples R China
[2] E China Normal Univ, Dept Math, Shanghai Key Lab PMMP, 500 Dongchuan Rd, Shanghai 200241, Peoples R China
来源：
RAMANUJAN JOURNAL | 2016年 / 40卷 / 02期
关键词：
Binomial coefficients; Congruence; WZ method;
D O I：
10.1007/s11139-015-9687-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For any prime p > 3 we prove that Sigma(k=0) (p-1) 3k+1/(-8)(k) ((2k)(k))(3) equivalent to p (-1/p) + p(3) Ep-3 (mod p(4)), where E-0, E-1, E-2, ... are Euler numbers and (./p) is the Legendre symbol. This result confirms a conjecture of Z.-W. Sun. We also re-prove that for any odd prime p, Sigma (k=0) (p-1/2) 6k+1/(-512)(k) ((2k)(k))(3) equivalent to p (-2/p) (mod p(2)) using WZ method.
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页码：237 / 244
页数：8
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