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Let $a$ and $b$ be positive integers,
give a necessary and sufficient condition on $b$ so that there exists an integer $k$ such that $S(ka)=b$
where $S(x):=$ the sum of digits of $x$ in base $10$

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  • $\begingroup$ What have you tried and where did you find this problem? If you list your attempts in the question we will be better able to help you. $\endgroup$ – Carl Schildkraut Oct 22 '18 at 20:37
  • $\begingroup$ I've tried using congruence modulo $9$ because $S(x)=x[9]$ for all $x$ but it wasn't enouph $\endgroup$ – K.Elias Oct 22 '18 at 21:40

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