Problem 294
Sum of digits - experience #23

For a positive integer k, define d(k) as the sum of the digits of k in its usual decimal representation. Thus d(42) = 4+2 = 6.

For a positive integer n, define S(n) as the number of positive integers k n with the following properties :

  • k is divisible by 23 and
  • d(k) = 23.
You are given that S(9) = 263626 and S(42) = 6377168878570056.

Find S(1112) and give your answer mod 109.

These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK