Journal of Mathematical Sciences

, Volume 233, Issue 5, pp 626–634 | Cite as

On p-Adic Approximation of Sums of Binomial Coefficients

  • R. R. Aidagulov
  • M. A. Alekseyev


We propose higher-order generalizations of Jacobsthal’s p-adic approximation for binomial coefficients. Our results imply explicit formulas for linear combinations of binomial coefficients \( \left(\underset{p}{ip}\right)\left(i=1,2,\dots \right) \)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. B. Fuks and M. B. Fuks, “Arithmetics of binomial coefficients,” Kvant, No. 6, 17–25 (1970).Google Scholar
  2. 2.
    S. B. Gashkov and V. N. Chubarikov, Arithmetics. Algorithms. Computational Complexity [in Russian], Vysshaya Shkola, Moscow (2000).Google Scholar
  3. 3.
    A. Granville. “Arithmetic properties of binomial coefficients. I. Binomial coefficients modulo prime powers,” Can. Math. Soc. Conf. Proc., 20, 253–275 (1997).MathSciNetzbMATHGoogle Scholar
  4. 4.
    R. Meštrović, Lucas’ Theorem: Its Generalizations, Extensions and Applications (1878–2014), arXiv: 1409.3820 (2014).Google Scholar
  5. 5.
    The OEIS Foundation: The On-Line Encyclopedia of Integer Sequences,
  6. 6.
    E. B. Vinberg, “Amazing arithmetic properties of binomial coefficients,” Mat. Prosv. Ser. 3, No. 12, 33–42 (2008).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • R. R. Aidagulov
    • 1
  • M. A. Alekseyev
    • 2
  1. 1.Moscow State UniversityMoscowRussia
  2. 2.George Washington UniversityAshburnUSA

Personalised recommendations