# Kummer's theorem

In mathematics, Kummer's theorem on binomial coeffients gives the highest power of a prime number p dividing a binomial coefficient. In particular, it asserts that given integers n ≥ m ≥ 0 and a prime number p, the maximum integer k such that pk divides the binomial coefficient $\tbinom n m$ is equal to the number of carries when m is added to n − m in base p.