For every real positive integer can be written as . For example, .
For every real positive integer , let denotes the sum of the digits of . For example, .
Question 1. For real positive integer , prove that is divisible by .
Question 2. From Q1, please explain why is divisible by if and only if is divisible by
Question 3. Let and be two positive real integer. And let be a number that is obtained by concatenating and . For example, if and , then . Prove that is divisible by . And also, prove that .
Question 4. A sequence defined as written below.
For every positive integer , prove that is not divisible by .
Question 5. Based on the sequence from Q4, among , how many number are there that are divisible by ?