The Number of Binomial Coefficients Divisible by a Fixed Power of a Prime

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There are binomial coefficients for every non-negative integer . Choose a prime number , and split the binomial coefficients into sets according to the highest power of that divides them. This Demonstration uses a combinatorial formula to compute the sizes of these sets. The first set is made up of the binomial coefficients not divisible by .

Contributed by: Oleksandr Pavlyk (March 2011)
Open content licensed under CC BY-NC-SA


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Details

W.B. Everett, "Number of Binomial Coefficients Divided by a Fixed Power of a Prime," arXiv.org, submitted Oct 8, 2007, http://arxiv.org/abs/0710.1468.



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