Cyclotomic Equation
The equation
where solutions
are the Roots of Unity sometimes called de MoivreNumbers. Gauß 
showed that the cyclotomic equation can be reduced to solving a series ofQuadratic Equations whenever 
is a Fermat Prime. Wantzel (1836) subsequently showedthat this condition is not only Sufficient, but also Necessary. An ``irreducible'' cyclotomic equation is anexpression of the form
where
is Prime. Its Roots 
satisfy 
.See also Cyclotomic Polynomial, de Moivre Number, Polygon, Primitive Root of Unity
References
Courant, R. and Robbins, H. What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 99-100, 1996. Scott, C. A. ``The Binomial Equation Wantzel, M. L. ``Recherches sur les moyens de reconnaître si un Problème de Géométrie peut se résoudre avec la règle et le compas.'' J. Math. pures appliq. 1, 366-372, 1836.
.'' Amer. J. Math. 8, 261-264, 1886.
- Obtuse Angle
- Obtuse Triangle
- Ochoa Curve
- Octacontagon
- Octadecagon
- Octagon
- Octagonal Number
- Octagram
- Octahedral Graph
- Octahedral Group
- Octahedral Number
- Octahedron
- Octahedron 5-Compound
- Octahemioctacron
- Octahemioctahedron
- Octakaidecagon
- Octal
- Octant
- Octatetrahedron
- Octic Surface
- Octillion
- Octodecillion
- Octonion
- Odd Function
- Odd Number