Prove that a number that consists of $3^n$ ones is divisible by $3^n$ I can't even make sense of this question. Isn't this just like asking, "Prove that 3 is divisible by 3." Isn't any number divisible by itself? Is this all there is to this question—it seems like there must be more to it.

What is meant is show that $111$ (so onehundred eleven) is divisible by $3^1$, and $111111111$ (the number with $3^2= 9$ times the digit $1$) is divisible by $3^2 = 9$ and so on.
The number is written using $3^n$ times the digit $1$.
Not, as you assume, $1+1+1$ and so on. This would indeed be obvious.
