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)
(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 9n3.
C=1+(9n3)/S(N+3).
Edited on May 29, 2016, 5:16 am

Posted by armando
on 20160529 05:10:59 