On p-adic approximation of sums of binomial coefficients

Rustem R. Aidagulov, Max A. Alekseyev

Published 2016-02-08Version 1

We propose higher-order generalizations of Jacobsthal's p-adic approximation for binomial coefficients. Our results imply explicit formulae for linear combinations of binomial coefficients $\binom{ip}{p}$ (i=1,2,...) that are divisible by arbitrarily large powers of prime p.