Let m and n be positive integers, and let p be a prime. Let T(x) = Φpm (Φ2n(x)), where Φk(x) is the cyclotomic polynomial of index k. In this article, we prove that T(x) is irreducible over Q and that
{1, θ, θ2, ..., θ2n-1pm-1(p-1)-1}
is a basis for the ring of integers of Q(θ), where T(θ) = 0.
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