(a) Let a be a cube root of unity, and let b be a fifth root of unity. Prove that ab is a \(15^{th}\)root of unity.

(b) Let a be a primitive cube root of unity, and b be a primitive fifth root of unity. Prove that ab is a primitive \(15^{th}\)root of unity.

(c) Let a be primitive fourth root of unity, and b be a primitive sixth root of unity. Is ab necessarily a primitive \(24^{th}\)root of unity?

brinlin Jul 18, 2021