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Digit Sum Equation Puzzle (Posted on 2016-05-28) Difficulty: 3 of 5
N is a positive integer and S(N) denotes the sum of the digits.

Find all values of a positive integer constant C such that:
S(N) = C*S(N+3)

No Solution Yet Submitted by K Sengupta    
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re: A more full solution. Comment 5 of 5 |
(In reply to A more full solution. by Jer)

That's good. 


Perhaps the summary is:
Be n a positive integer, the condition only occurs when, for some n, N is congruent with 10^n -3 or 10^n -2 or 10^n -1 (mod 10^n).

And exist a C value when S(N+3) is a divisor of 9n-3. 

C=1+(9n-3)/S(N+3).

Edited on May 29, 2016, 5:16 am
  Posted by armando on 2016-05-29 05:10:59

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