The Ramanujan Journal

, Volume 48, Issue 1, pp 173–189 | Cite as

Finding more divisibility properties of binomial sums via the WZ method

  • Brian Y. SunEmail author


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.


Hypergeometric function Divisibility Binomial coefficients Binomial sums The WZ method 

Mathematics Subject Classification

11A05 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.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and System ScienceXinjiang UniversityUrumqiPeople’s Republic of China

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