# 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 $\varkappa\acute{\upsilon}\varkappa\lambda{o}\varsigma$ ‘circle’,  $\tau\acute{o}\mu{o}\varsigma$ ‘part’).

Title binomial equation BinomialEquation 2013-03-22 17:46:05 2013-03-22 17:46:05 pahio (2872) pahio (2872) 9 pahio (2872) Definition msc 11C08 msc 12E05 Binomial CalculatingTheNthRootsOfAComplexNumber RootOfUnity cyclotomic equation