When the natural numbers are written one after another in an increasing way, you get an infinite succession of digits 123456789101112.... Denote Ak the number formed by the first k digits of this sequence . Prove that for all positive integer n there is a positive integer m which simultaneously verifies the following three conditions:
(i) n divides Am,
(ii) n divides m,
(iii) n divides the sum of the digits of Am. number theorysum of digitsSequenceDivisibility