# automorphic number

Given a base $b$ integer

$$n=\sum _{i=1}^{k}{d}_{i}{b}^{i-1}$$ |

where ${d}_{1}$ is the least significant digit and ${d}_{k}$ is the most significant, if it’s also the case that the $k$ least significant digits of $m{n}^{2}$ are the same of those of $n$, then $n$ is called an automorphic number, or an $m$-automorphic number.

Neither $b$ nor $b+1$ can be 1-automorphic in base $b$.

Title | automorphic number |
---|---|

Canonical name | AutomorphicNumber |

Date of creation | 2013-03-22 16:20:17 |

Last modified on | 2013-03-22 16:20:17 |

Owner | CompositeFan (12809) |

Last modified by | CompositeFan (12809) |

Numerical id | 5 |

Author | CompositeFan (12809) |

Entry type | Definition |

Classification | msc 11A63 |