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Binomial Equation

Binomial equation is an algebraic equation of the simple type

$\displaystyle x^n-a = 0$

where

belongs to a certain field (or sometimes to a certain ring) and

is the unknown (or the indeterminate) of the equation. Solving the binomial equation means taking the

The binomial equation is written also

$\displaystyle x^n = a.$

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

A special case of the binomial equation is the cyclotomic equation

$\displaystyle x^n-1 = 0.$

This name comes from the fact that the roots of the equation divide the unit circle in the complex plane into

equally long arcs (Greek $\varkappa\acute{\upsilon}\varkappa\lambda{o}\varsigma$ `circle', $\tau\acute{o}\mu{o}\varsigma$ `part').

1	Complex
1	Field
1	Positive
1	Integer
1	Ring
1	Group
1	Equation
2	Proof Of Uniqueness Of Center Of A Circle
2	Path Connected
2	Indeterminate
4	Unit Disk
4	Nth Root
8	Algebraic Equation