MathDB

Distinct roots of unity

Source:

March 21, 2006

trigonometrynumber theoryleast common multiplegreatest common divisormodular arithmeticcomplex numbersrelatively prime

Problem Statement

The sets

A = \{z : z^{18} = 1\}

and

B = \{w : w^{48} = 1\}

are both sets of complex roots of unity. The set

C = \{zw : z \in A \ \text{and} \ w \in B\}

is also a set of complex roots of unity. How many distinct elements are in

C