On a theorem of Scholz on the class number of quadratic fields. (English) Zbl 1062.11071

Let \(K= \mathbb{Q}(\sqrt{pq})\) where \(p\) and \(q\) are distinct primes such that \(p\equiv q\pmod 4\). In the note under review, the author gives another proof of a classical result of A. Scholz, and determines the exact power of 2 dividing the class number of \(K\) using a theorem on the solvability of \(ax^2+ by^2= z^2\).


11R29 Class numbers, class groups, discriminants
11R11 Quadratic extensions
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