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# repdigit

Given base $b$, a number of the form $d({{b^{n}-1}\over{b-1}})$ for $n>0$ and $0<d<b$ is written using using the digit $d$ only, $n$ times in that base and is therefore a repdigit. The term, short for ”repeated digit,” is credited to Beiler’s book Recreations in the theory of numbers, in chapter 11.

When $d=1$, the resulting repdigit is called a repunit. Only repunits can also be prime (and even then they are rare). No other repdigit can be prime since it is obvious that it is a multiple of a repunit.

In a trivial way, all repdigits are palindromic numbers.

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(v5) by CompositeFan 2013-03-22