Division of natural numbers

Question

How can I prove that $9|n$ if and only if $9$ divides the sum of the digits of $n$, where $n \in \mathbb{N}$

Try inducting on the number of digits of the natural number – Stella Biderman Jan 18 '15 at 21:00 — Stella Biderman, Jan 18 '15 at 21:00

score -1 · Answer 1 · answered Jan 18 '15 at 21:00

-1

Hint : $10^n\equiv 1\ (\ mod\ 9\ )$ for all $n\ge 0$.

answered Jan 18 '15 at 21:00

Peter

1 Answers1