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.

Generalization :
If modulo order ord$_{p^k}a=d\implies a^d\equiv1\pmod{p^k},a^d=1+p^k\cdot c$ for some integer $c$ and $p$ is any integer
$\implies a^{pd}=(a^d)^p=(1+p^k\cdot c)^p\equiv1\pmod{p^{k+1}}$
Here $a=10,p=3,k=2,d=1$
So by mathematical induction, $10^n\equiv1\pmod{3^{n+1}}$ for integer $n\ge1$
