Let be a primitive th root of unity and let . Prove that is a primitive th root of unity.
Certainly . Now if , we have , and so divides . So is the order of , and thus is a primitive th root of unity.
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Let be a primitive th root of unity and let . Prove that is a primitive th root of unity.
Certainly . Now if , we have , and so divides . So is the order of , and thus is a primitive th root of unity.
On these pages you will find a slowly growing (and poorly organized) list of proofs and examples in abstract algebra.
No doubt these pages are riddled with typos and errors in logic, and in many cases alternate strategies abound. When you find an error, or if anything is unclear, let me know and I will fix it.