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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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