Key points are not available for this paper at this time.
We present novel combinatorial proofs for some cases of a classic result of Kummer, that the highest power of p dividing the binomial coefficient n choose m equals the number of carries when adding m to n-m in base p. We prove the case p=2 by considering permutations of binary vectors, and extend this approach to arbitrary primes for the case of no carries.
Michael J. Collins (Wed,) studied this question.