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June 5th, 2009, 06:25 PM   #1
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Every quadratic field is contained in a cyclotomic field

This is a well known theorem.
In perticular, the mth quadratic field, for m squarefree, is contained in the dth cyclotomic field, where , the discriminant of the ring of algebraic integers in the mth quadratic field.

Now my question is : is the dth cyclotomic field the cyclotomic field with least d containing the mth quadratic field?
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