Question 76
For any positive integer $n$, call the number obtained by concatenating 2012 decimal copies of $n$ the repeated number of $n$. For example, the repeated number of 314 is $314314314\ldots314$, with “314” repeated 2012 times.
a) Determine all positive integers $m$ whose repeated number is divisible by 9.
b) Determine all positive integers $m$ whose repeated number is divisible by 11.
a) Determine all positive integers $m$ whose repeated number is divisible by 9.
b) Determine all positive integers $m$ whose repeated number is divisible by 11.