# Multiple of $n$ and the sum of its digits is $k\geq n$.

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 $k$.

• Do you have to find one pair of $n,k$ as in the title, or you have to prove "there exists ..." for all pairs of such $n, k$? – peterwhy Nov 23 '14 at 14:11
• For a fixed n and every k there exists a positive integer – HeatTheIce Nov 23 '14 at 14:15
• I asked this a couple of years agosto, ley me ser if O can find It. – Jorge Fernández Hidalgo Jan 28 '17 at 21:10