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arXiv · 1503.03418

Note on super congruences modulo $p^2$

Zhi-Hong Sun
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Abstract

Let $p$ be an odd prime, and let $m$ be an integer with $p\nmid m$. In this paper show that $$\sum_{k=0}^{p-1}\frac{\binom{2k}k\binom ak\binom{-1-a}k}{m^k} \equiv 0\pmod p \quad\hbox{implies}\quad\sum_{k=0}^{p-1}\frac{\binom{2k}k\binom ak \binom{-1-a}k}{m^k}\equiv 0\pmod {p^2}.$$

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Zhi-Hong Sun. 2015-03-11. Note on super congruences modulo $p^2$. https://arxiv.org/abs/1503.03418

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