Let , then is one of the primitive m th roots of unity.

a) Show that if m|n.

Proof.

Let mt = n for some integer t.

Pick an element , with a and b rational numbers.

Then it equals to Now, is this element in ? I just don't know if is a rational number.

b) Show that .

Proof.

There is a theorem that state: Let be a primitive pth root of unity, p an odd prime. if

Now, is a primitive pth roof of unity?

Thank you.