Proof of a Dwork-type supercongruence by induction
In this paper we prove a Dwork-type supercongruence: for any prime $ p\geq3 $ and integer $ r\geq 1 $, $ \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*}...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2021-08-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2021671?viewType=HTML |