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Article overview
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Some supercongruences modulo $p^2$ | Zhi-Hong Sun
; | Date: |
5 Jan 2011 | Abstract: | Let $p>3$ 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 | Services: | Forum | Review | PDF | Favorites |
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