# repdigit

Given base $b$, a number of the form $d(\frac{{b}^{n}-1}{b-1})$ for $n>0$ and $$ 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 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^{}.

Title | repdigit |
---|---|

Canonical name | Repdigit |

Date of creation | 2013-03-22 16:20:14 |

Last modified on | 2013-03-22 16:20:14 |

Owner | CompositeFan (12809) |

Last modified by | CompositeFan (12809) |

Numerical id | 5 |

Author | CompositeFan (12809) |

Entry type | Definition |

Classification | msc 11A63 |