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
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
is prime. Its roots 
satisfy 