# binomial equation

Binomial equation is an algebraic equation of the

$${x}^{n}-a=0$$ |

where $n$ is a positive integer, $a$ belongs to a certain field (or sometimes to a certain ring) and $x$ is the unknown (or the indeterminate) of the equation. Solving the binomial equation means taking the $n$th root (http://planetmath.org/NthRoot) of $a$.

The binomial equation is written also

$${x}^{n}=a.$$ |

Such a binomial equation may be examined in a group, too.

A special case of the binomial equation is the cyclotomic equation

$${x}^{n}-1=0.$$ |

This name comes from the fact that the roots (http://planetmath.org/Equation) of the equation the unit circle in the complex plane^{} into $n$ equally long arcs (Greek $\varkappa \stackrel{\xb4}{\upsilon}\varkappa \lambda o\varsigma $ ‘circle’, $\tau \stackrel{\xb4}{o}\mu o\varsigma $ ‘part’).

Title | binomial equation |
---|---|

Canonical name | BinomialEquation |

Date of creation | 2013-03-22 17:46:05 |

Last modified on | 2013-03-22 17:46:05 |

Owner | pahio (2872) |

Last modified by | pahio (2872) |

Numerical id | 9 |

Author | pahio (2872) |

Entry type | Definition |

Classification | msc 11C08 |

Classification | msc 12E05 |

Related topic | Binomial |

Related topic | CalculatingTheNthRootsOfAComplexNumber |

Related topic | RootOfUnity |

Defines | cyclotomic equation |