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Diophantine equations and class numbers of real quadratic fields. (English) Zbl 1014.11069
Let \(d\) be a positive integer that is square free, and let \(h(d)\) denote the class number of the real quadratic field \(\mathbb{Q}(\sqrt{d})\). In the present paper the authors give some results concerning the divisibility of \(h(d)\) while \(d\) satisfies \(da^2= 1+4b^2 k^{2n}\), where \(a,b,k,n\) are positive integers satisfying \(k>1\) and \(n>1\).

MSC:
11R29 Class numbers, class groups, discriminants
11R11 Quadratic extensions
11D41 Higher degree equations; Fermat’s equation
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