Let $N$ be a four digit number, and $N'$ be $N$ with its digits reversed. Prove that $N-N'$ is divisible by $9$. Prove that $N+N'$ is divisible by $11$.
I let $N=abcd$ and $N'=dcba$
but I dont see how I can proceed to show that either the sum or difference is divisble by 11 or 9.
Any ideas on how to start this problem?