The Number of Binomial Coefficients Divisible by a Fixed Power of a Prime
The Number of Binomial Coefficients Divisible by a Fixed Power of a Prime
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 .
n+1
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n
p
n+1
p
p