| 1. | It uses Lucas sequences to perform exponentiation in a quadratic field.
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| 2. | The following table shows some orders of small discriminant of quadratic fields.
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| 3. | It covers elementary number theory, Dirichlet's theorem, and quadratic fields.
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| 4. | The theory for real quadratic fields is essentially the theory of Pell's equation.
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| 5. | This occurs if and only if the class number of the corresponding quadratic field is one.
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| 6. | Before that in his dissertation used Hilbert modular forms to study abelian extensions of real quadratic fields.
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| 7. | This result is ineffective, as indeed was the result on quadratic fields on which it built.
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| 8. | Although the quadratic integers belonging to a given quadratic field form a minimal polynomial of degree four.
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| 9. | Chapter 5 contains Dirichlet's derivation of the class number formula for real and imaginary quadratic fields.
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| 10. | While all quadratic fields are monogenic, already among cubic fields there are many that are not monogenic.
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