Some Congruences Involving Binomial Coefficient and Fermat Quotient

Wei-Wei Qi

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arXiv · 2512.01385

Some Congruences Involving Binomial Coefficient and Fermat Quotient

Wei-Wei Qi

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Abstract

In this paper, we investigate some congruences involving sums of $\frac{d^{-k}{x\choose k}{x+k\choose k}}{{2k \choose k}}$, where $x$ be a $p$-adic integer, $k$ be a non-negative integer, and $d$ $(d\neq 0)$ be a rational number.

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Wei-Wei Qi. 2025-12-01. Some Congruences Involving Binomial Coefficient and Fermat Quotient. https://arxiv.org/abs/2512.01385

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