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How to find minimal positive integer divisible by n, with the sum of digits equal to n.?

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How to find minimal positive integer divisible by n, with the sum of digits equal to n.?

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  1. Answer:

    1

    1 is divisible by 1

    Sum of its digits = 1


  2. If n can vary, see Puzzling's solution.

    If n is fixed, then note that some values of n won't work.  For instance, if n=11, then I believe that no integer satisfies the requirements.
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