Show that for every positive integers $k\geq n$, with $n$ not divisible by $3$, there is a positive integer divisible by $n$ and such that the sum of his digits is $k$.
2026-04-01 20:54:58.1775076898
Multiple of $n$ and the sum of its digits is $k\geq n$.
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IMO ShortList 1999, number theory problem 5 http://artofproblemsolving.com/community/c6h19765p131819