Question
Let $m$ and $n$ be relatively prime positive integers. Prove that the splitting field of $x^{m n}-1$ over $Q$ is the same as the splitting field of $\left(x^{m}-1\right)\left(x^{n}-1\right)$ over $Q$
Step 1
These roots can be expressed as \( \zeta_k = e^{2\pi i k / mn} \) for \( k = 0, 1, 2, \ldots, mn - 1 \). Show more…
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