Let

be positive integers such that n is not divisible by 3 and

. Prove that there exists a positive integer

which is divisible by

and the sum of its digits in decimal representation is

.
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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 $k$.