Two new $q$-supercongruences arising from Carlitz’s identity
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- by Ji-Cai Liu and Wei-Wei Qi
- Proc. Amer. Math. Soc. 152 (2024), 1733-1741
- DOI: https://doi.org/10.1090/proc/16705
- Published electronically: February 14, 2024
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Abstract:
From Carlitz’s identity, we deduce two new $q$-supercongruences modulo the square of a cyclotomic polynomial, which were originally conjectured by Guo. These results establish new $q$-analogues of a supercongruence of Sun.References
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Bibliographic Information
- Ji-Cai Liu
- Affiliation: Department of Mathematics, Wenzhou University, Wenzhou 325035, People’s Republic of China
- ORCID: 0000-0002-8618-2305
- Email: jcliu2016@gmail.com
- Wei-Wei Qi
- Affiliation: Department of Mathematics, Wenzhou University, Wenzhou 325035, People’s Republic of China
- Email: wwqi2022@foxmail.com
- Received by editor(s): July 9, 2023
- Received by editor(s) in revised form: September 9, 2023, and September 23, 2023
- Published electronically: February 14, 2024
- Additional Notes: The first author was supported by the National Natural Science Foundation of China (grant 12171370).
The first author is the corresponding author. - Communicated by: Mourad Ismail
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 1733-1741
- MSC (2020): Primary 33D15, 11A07, 11B65
- DOI: https://doi.org/10.1090/proc/16705
- MathSciNet review: 4709239