Finding more divisibility properties of binomial sums via the WZ method
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In recent years, we have witnessed numerous new results on divisibility properties concerning binomial sums. Many conjectures and results were proposed by Z.-W. Sun. Some of these conjectures were proved by himself, and also by some scholars such as V.J.W. Guo, G.S. Mao, B. He, and Y.P. Mu. Motivated by their work, we study the WZ method and its applications to prove divisibility properties of binomial sums. In this paper, we propose a method which can be used to explore more such divisibility properties. Additionally, we give some generalized divisibility properties which can imply those divisibility properties established by Z.-W. Sun and B. He.
KeywordsHypergeometric function Divisibility Binomial coefficients Binomial sums The WZ method
Mathematics Subject Classification11A05 11A07 05A10 11B65
We are extremely thankful to the referee for helpful suggestions and comments, which greatly helped to improve the presentation of this paper.
- 16.Sun, Z.-W.: Open conjectures on congruences. arXiv:0911.5665