Let
![n,k](/media/m/e/e/7/ee71124e8ab93077f18aac50da5c293c.png)
be positive integers such that n is not divisible by 3 and
![k \geq n](/media/m/e/5/5/e55b0a0f68412177ff33120dfcd2a8df.png)
. Prove that there exists a positive integer
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
which is divisible by
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
and the sum of its digits in decimal representation is
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
.
%V0
Let $n,k$ be positive integers such that n is not divisible by 3 and $k \geq n$. Prove that there exists a positive integer $m$ which is divisible by $n$ and the sum of its digits in decimal representation is $k$.