perplexus.info :: Just Math : Digit Sum Equation Puzzle

Digit Sum Equation Puzzle (Posted on 2016-05-28)

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

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

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

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (24)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info