Question

Find the smallest two digit natural number n such that sum of digits of 10^n-n) is divisible by 170.​

Answer 1

Answer:

Find the smallest two digit natural number n such that sum of digits of 10^n-n) is divisible by 170.

Answer 2

Step-by-step explanation:

The digit sum of N−1 is somewhere between 1 and 17 (inclusive). So our two-digit number must necessarily be such that 9N is within "reach" of a multiple of 170. The possible values for 9N and thus N is therefore

9N171180342351513522684693855864N19203839575876779596Digit sum9101011111212131314

We see that the N for which 9N minus the digit sum of N−1 is a multiple of 170 are the larger one in each "pair", which is to say

20,39,58,77,96