期刊
RAMANUJAN JOURNAL
卷 40, 期 2, 页码 237-244出版社
SPRINGER
DOI: 10.1007/s11139-015-9687-7
关键词
Binomial coefficients; Congruence; WZ method
类别
资金
- Natural Science Foundation of Inner Mongolia Autonomous Region [2011BS1003]
- research project for science and technology of Colleges and Universities in Inner Mongolia Autonomous Region [NJSY12073]
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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