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Lemmermeyer, Franz
2021.
Quadratic Number Fields.
p.
209.
Published online by Cambridge University Press: 28 September 2015
Using the elements of order four in the narrow ideal class group, we construct generators of the maximal elementary $2$-class group of real quadratic number fields with even discriminant which is a sum of two squares and with fundamental unit of positive norm. We then give a characterization of when two of these generators are equal in the narrow sense in terms of norms of Gaussian integers.