Skip to main content
SpringerLink
Log in

On two supercongruences of double binomial sums

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

Abstract

In this note we confirm two conjectural supercongruences of double sums of binomial coefficients due to El Bachraoui.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. El Bachraoui, On Supercongruences for Truncated Sums of Squares of Basic Hypergeometric Series, Ramanujan J., online. https://doi.org/10.1007/s11139-019-00226-0

  2. V.J.W. Guo, Proof of some \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial. Results Math. 75, Art. 77 (2020)

  3. V.J.W. Guo, J.-C. Liu, \(q\)-Analogues of two Ramanujan-type formulas for \(1/\pi \). J. Differ. Equ. Appl. 24, 1368–1373 (2018)

    Article  MathSciNet  Google Scholar 

  4. V.J.W. Guo, M.J. Schlosser, Some new \(q\)-congruences for truncated basic hypergeometric series: even powers. Results Math. 75, Art. 1 (2020)

  5. V.J.W. Guo, W. Zudilin, A \(q\)-microscope for supercongruences. Adv. Math. 346, 329–358 (2019)

    Article  MathSciNet  Google Scholar 

  6. L. Li, S.-D. Wang, Proof of a \(q\)-supercongruence conjectured by Guo and Schlosser. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114, Art. 190 (2020)

  7. J.-C. Liu, Z.-Y. Huang, A truncated identity of Euler and related \(q\)-congruences. Bull. Aust. Math. Soc. https://doi.org/10.1017/S0004972720000301

  8. J.-C. Liu, On a congruence involving \(q\)-Catalan numbers. C. R. Math. Acad. Sci. Paris 358, 211–215 (2020)

    MathSciNet  MATH  Google Scholar 

  9. J.-C. Liu, F. Petrov, Congruences on sums of \(q\)-binomial coefficients. Adv. Appl. Math. 116, Art. 102003 (2020)

Download references

Acknowledgements

The first author was supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant 19KJB110006). The second author was supported by the National Natural Science Foundation of China (Grant 11801417).

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Huaiyin Normal University, Huai’an, 223300, People’s Republic of China

    Long Li

  2. Department of Mathematics, Wenzhou University, Wenzhou, 325035, People’s Republic of China

    Ji-Cai Liu

Authors
  1. Long Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ji-Cai Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ji-Cai Liu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, L., Liu, JC. On two supercongruences of double binomial sums. Period Math Hung 83, 159–164 (2021). https://doi.org/10.1007/s10998-020-00377-4

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10998-020-00377-4

Keywords

Mathematics Subject Classification

Search

Navigation