# 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

n |

k |

n

p

n+1

p

p