Abstract
Let $p$ and $q$ be distinct primes such that $p \equiv q \pmod{4}$ and consider the quadratic field $K = \mathbf{Q}(\sqrt{pq})$. In this paper, we shall investigate the class group and determine the exact power of 2 dividing the class number of $K$ using the theory of ideals and a theorem on the solvability of $ax^2 + by^2 = z^2$.
Citation
Fidel R. Nemenzo. "On a theorem of Scholz on the class number of quadratic fields." Proc. Japan Acad. Ser. A Math. Sci. 80 (2) 9 - 11, Feb. 2004. https://doi.org/10.3792/pjaa.80.9
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