Let for all $k \in {\mathbb N}$ $k$'s sum of the digits is $T(k)$. If a natural number $n$ such that $T(n)=T(1997n)$, prove that $$9\mid n$$
Source:
Tags: number theory
Let for all $k \in {\mathbb N}$ $k$'s sum of the digits is $T(k)$. If a natural number $n$ such that $T(n)=T(1997n)$, prove that $$9\mid n$$