It uses Lucas sequences to perform exponentiation in a quadratic field.
Gauss conjectures that there are infinitely many real quadratic fields with class number one.
The contrasting case of real quadratic fields is very different, and much less is known.
It may well be the case that class number 1 for real quadratic fields occurs infinitely often.
In general, the unit group of a real quadratic field is always infinite (of rank 1).
This result is ineffective, as indeed was the result on quadratic fields on which it built.
There is exactly one quadratic field for every fundamental discriminant D 1, up to isomorphism.
This therefore gives us the precise information about which quadratic field lies in Q(ζ).
The stick people had set up a number of lamps, forming the outline of a large quadratic field.
The theory for real quadratic fields is essentially the theory of Pell's equation.
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