Note on the class numbers of certain real quadratic fields
Let \(n\) and \(a\) be integers, \(n\geq 2\), \(a\geq 3\), \(a\) odd, and \(K_{a,n}= \mathbb{Q}(\sqrt{a^{2n}+ 4})\). Then \(\alpha= {1\over 2}(a^n+ 2+ \sqrt{a^{2n}+ 4})\) is an integer of \(K_{a,n}\) and there exists an ideal \({\mathfrak A}\) of \(K_{a,n}\) such that \((\alpha)= {\mathfrak A}^n\). The author proves that the order of the ideal class \([{\mathfrak A}]\) equals \(n\) and as a consequence of this statement he presents the main result of this paper that the class number of \(K_{a,n}\) is divisible by \(n\).
scientific article; zbMATH DE number 2063950