Corpus ID: 214713515

# A $p$-congruence for a finite sum of products of binomial coefficients

@article{Gy2020AF,
title={A \$p\$-congruence for a finite sum of products of binomial coefficients},
author={Ren'e Gy},
journal={arXiv: Number Theory},
year={2020}
}
• Ren'e Gy
• Published 2020
• Mathematics
• arXiv: Number Theory
• For any prime $p$ and any natural numbers $\ell, n$ such that $p$ does not divide $n$, it holds that $\sum_{i\ge \ell+1}(-1)^i {\lfloor \frac{n}{p}\rfloor p \choose i}{n-1+i(p-1) \choose n-1+\ell(p-1)} \equiv 0\bmod p$. Our proof involves Stirling numbers.

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