so looked more into it lol, this is what i have,
10^k+1 -1 = 10^k 10^1 - 1
10^k-1 = 9q into 10^k = 9q+1
10^k+1 -1 = 10^k 10-1
and that has a factor of 9 so it is divisible
lol, you cannot possibly be serious about any of this.
None of that after the first line has any truth in fact.
You are truly challenged by very very basic algebra.