# index of an integer with respect to a primitive root

###### Definition.

Let $m\mathrm{>}\mathrm{1}$ be an integer such that the integer $g$ is a primitive root^{} for $m$. Suppose $a$ is another integer relatively prime to $g$. The index of $a$ (to base $g$) is the smallest positive integer $n$ such that ${g}^{n}\mathrm{\equiv}a\mathrm{mod}m$, and it is denoted by $\mathrm{ind}\mathit{}a$ or ${\mathrm{ind}}_{g}\mathit{}a$.

If $m$ has a primitive root the index with respect to a primitive root is a very useful tool to solve polynomial congruences modulo $m$.

Title | index of an integer with respect to a primitive root |
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Canonical name | IndexOfAnIntegerWithRespectToAPrimitiveRoot |

Date of creation | 2013-03-22 16:20:50 |

Last modified on | 2013-03-22 16:20:50 |

Owner | alozano (2414) |

Last modified by | alozano (2414) |

Numerical id | 4 |

Author | alozano (2414) |

Entry type | Definition |

Classification | msc 11-00 |