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arXiv · 1602.02632

On p-adic approximation of sums of binomial coefficients

Rustem R. Aidagulov·Max A. Alekseyev
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Abstract

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 $\binom{ip}{p}$ ($i=1,2,\dots$) that are divisible by arbitrarily large powers of prime $p$.

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Rustem R. Aidagulov, Max A. Alekseyev. 2018-08-30. On p-adic approximation of sums of binomial coefficients. https://doi.org/10.1007/s10958-018-3948-0

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