Question

Given two natural numbers `k`  and `m` that differ only in the order of their digits (that is, one is obtained from the other by swapping the order of the digits).

a. Prove that the sum of the digits of `2k` is equal to the sum of the digits of `2m`.

b. Prove that if `k` and `m` are even, then the sum of the digits of \(k\over 2\)  is equal to the sum of the digits of \({m \over 2}\).

c. Prove that the sum of the digits of `5k` is equal to the sum of the digits of `5m`.