Let $R_n$ denote the repunit with $n$ ones. So $R_1=1, R_2=11, R_3=111, ...$.
I know that $R_n = (10^n - 1)/9$ and I want to show that
$R_n$ divides $R_m$ iff $n$ divides $m$.
How would I go about doing that? I tried to use the definition of divisibility but I end up with $log_{10}$ terms and there wasn’t much I could do after that.