New congruences involving products of two binomial coefficients

  • Guo-Shuai Mao
  • Zhi-Wei SunEmail author


Let \(p>3\) be a prime and let a be a positive integer. We show that if Open image in new window or \(a>1\), then with \((-)\) the Jacobi symbol, which confirms a conjecture of Z.-W. Sun. We also establish the following new congruences:


Central binomial coefficients Congruences Legendre symbol 

Mathematics Subject Classification

Primary 11B65 11B68 Secondary 05A10 11A07 



The authors would like to thank Prof. Hao Pan and the anonymous referee for helpful comments.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsNanjing UniversityNanjingPeople’s Republic of China

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