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Proof of a Dwork-type supercongruence by induction
- Source :
- AIMS Mathematics, Vol 6, Iss 10, Pp 11568-11583 (2021)
- Publication Year :
- 2021
- Publisher :
- AIMS Press, 2021.
-
Abstract
- In this paper we prove a Dwork-type supercongruence: for any prime $ p\geq3 $ and integer $ r\geq 1 $, \begin{document}$ \begin{align*} \sum\limits_{k = 0}^{p^r-1}\frac{3k+1}{16^k}{\binom{2k}{k}}^3\equiv p\sum\limits_{k = 0}^{p^{r-1}-1}\frac{3k+1}{16^k}{\binom{2k}{k}}^3\pmod{p^{3r+1-\delta_{p, 3}}}, \end{align*} $\end{document} which extends a result of Guo and Zudilin.
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 6
- Issue :
- 10
- Database :
- OpenAIRE
- Journal :
- AIMS Mathematics
- Accession number :
- edsair.doi.dedup.....638f05ed29a2355d521dab1143375449