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15 August 2020
 
  » arxiv » 1101.1050

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Some supercongruences modulo $p^2$
Zhi-Hong Sun ;
Date 5 Jan 2011
AbstractLet $p>3$ be a prime, and let $m$ be an integer with $p mid m$. In the paper we prove some supercongruences concerning $$align &sum_{k=0}^{p-1}frac{inom{2k}kinom{3k}k}{54^k}, sum_{k=0}^{p-1}frac{inom{2k}kinom{4k}{2k}}{128^k}, sum_{k=0}^{p-1}frac{inom{3k}kinom{6k}{3k}}{432^k},
&sum_{k=0}^{p-1}frac{inom{2k}k^2inom{3k}{k}}{m^k}, sum_{k=0}^{p-1}frac{inom{2k}k^2inom{4k}{2k}}{m^k}, sum_{k=0}^{p-1}f{inom{2k}kinom{3k}{k}inom{6k}{3k}}{m^k}mod {p^2}.endalign$$ Thus we solve some conjectures of Zhi-Wei Sun and the author.
Source arXiv, 1101.1050
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