Proof of a supercongruence conjecture of He

Abstract

We here establish some supercongruence results concerning certain truncated hypergeometric series. As a consequence, we confirm a recent conjectural supercongruence [6, Conjecture1.3] of Bing He.

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Acknowledgements

Arijit Jana acknowledges the support received from Department of Science and Technology, Goverment of India, through an INSPIRE Fellowship (Award no. DST/INSPIRE Fellowship/2017/IF170327). Gautam Kalita is partially supported by a project (Grant Number: EMR/ 2016/005010) of SERB, Department of Science and Technology, Goverment of India, under Extra Mural Research Funding (Individual Centric).

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Correspondence to Gautam Kalita.

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Chetry, A.S., Jana, A. & Kalita, G. Proof of a supercongruence conjecture of He. Res. number theory 7, 21 (2021). https://doi.org/10.1007/s40993-021-00249-x

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Keywords

  • Hypergeometric series
  • Supercongruences
  • Gamma function

Mathematics Subject Classification

  • 11A07
  • 11D88
  • 33B15
  • 33C20