1. The problem statement, all variables and given/known data Let m be a positive integer and m' be an integer obtained from m by rearranging its digits. Prove that m-m' is a multiple of 9 2. Relevant equations Casting out 9's method 3. The attempt at a solution So I found that by applying the casting out 9's method on m and m'; the values are the same. This means that when one divides m by 9 and m' by 9; it is the same remainder. I'm wondering how do I use this to prove that 9 divides m-m'