## Cyclotomic Equation

The equation

where solutions are the Roots of Unity sometimes called de Moivre Numbers. Gauß showed that the cyclotomic equation can be reduced to solving a series of Quadratic Equations whenever is a Fermat Prime. Wantzel (1836) subsequently showed that this condition is not only Sufficient, but also Necessary. An irreducible'' cyclotomic equation is an expression 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 .'' Amer. J. Math. 8, 261-264, 1886.

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.