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arXiv · 2204.10132

Supercongruences for sums involving $\binom ak^m$

Zhi-Hong Sun
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Abstract

Let $p$ be an odd prime, and let $a$ be a rational $p$-adic integer with $a\not\equiv 0\pmod p$. In this paper, using WZ method we establish the congruences for $\sum_{k=0}^{p-1} \binom ak^2(-1)^k(1-\frac 2ak)$ modulo $p^2$ and $\sum_{k=0}^{p-1} \binom ak^r(1-\frac 2ak)^s$ modulo $p^4$, where $r\in\{3,4\}$ and $s\in\{1,3\}$.

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Zhi-Hong Sun. 2022-04-21. Supercongruences for sums involving $\binom ak^m$. https://arxiv.org/abs/2204.10132

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