Binomial equation is an algebraic equation of the simple type $$x^n-a = 0$$ 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 $n$ root 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 of the equation divide 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').