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
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