Can anyone help me with such task?
I'm preparing for my exam session and got stuck with that:
Prove, that for every natural number $n$, there exists another natural number $S$,
which is divisible by $n$ and its sum of digits (in decimal system) equals to $n$.
I presume that Chinese remainder theorem would be helpful here,
yet I don't know how to use it properly. Any ideas?
Thanks for your help