10

Part of 1990 AIME Problems

Problems(1)

Distinct roots of unity

Source:

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

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

trigonometrynumber theoryleast common multiplegreatest common divisormodular arithmeticcomplex numbersrelatively prime