Geodesic
On $p$-adic approximation of sums of binomial coefficients
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 1, pp. 37-48.

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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 $\binom{ip}{p}$ ($i=1,2,\ldots$) that are divisible by arbitrarily large powers of prime $p$. 
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R. R. Aidagulov; M. A. Alekseyev. On $p$-adic approximation of sums of binomial coefficients. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 1, pp. 37-48. http://geodesic.mathdoc.fr/item/FPM_2016_21_1_a2/

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