Let $n$ be a 3-digit number. Prove $9\mid n$ iff the digits of $n$ sum to a multiple of 9. I have convinced myself that this true, however I'm at a loss of where I should start with this proof. Looking at a similar proof with 3 instead of 9, I saw the use of the basis representation theorem, but I'm not 100% comfortable with that, so it was hard for me to follow. Is there a way to do this with mod?

Hint: $10\equiv1\pmod{9}    $.
