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