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. 

    References

    Publications referenced by this paper.
    SHOWING 1-4 OF 4 REFERENCES

    Concrete Mathematics

    • R. L. Graham, D. E. Knuth, O. Patashnik
    • Adison-Wesley Publishing Company, 2nd Edition
    • 1994
    VIEW 3 EXCERPTS
    HIGHLY INFLUENTIAL

    ), when p does not divide n, by Kummer theorem, p), since in this case the addition (n − p) + (p − 1) in base p has at least one carry

    • Now

    A three-parameters identity involving Stirling numbers of both kinds

    • M. Riedel
    • URL
    • 2020

    A three-parameters identity involving Stirling numbers of both kinds, URL (version

    • M Riedel