Repunit
= Repunit
{title2=$R_b(k)$}
A <repdigit> whose digits are all 1 in a specified <positional notation> of base $b$. Its value is the <geometric series> $R_b(k)=1+b+\cdots+b^{k-1}=(b^k-1)/(b-1)$. In base ten, appending one digit gives $R_{10}(k+1)=10R_{10}(k)+1$, so its <remainder> <modulo> $n$ can be computed by a <recurrence relation> without constructing the full <integer>.