On some congruences of certain binomial sums

被引：15

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.

引用

页码：237 / 244

页数：8

共 16 条

[1]

[Anonymous], 1862, Quart. J. Pure Appl. Math

[2]

[Anonymous], 1996, A=B.

[3]

Ekhad D., 1994, GEOMETRY ANAL MECH, P107

[4] DECISION PROCEDURE FOR INDEFINITE HYPERGEOMETRIC SUMMATION [J].