 Repunit

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.

A **repunit** is a type of number that consists entirely of the digit 1 repeated one or more times. The term "repunit" comes from "repeated unit.