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arXiv · 1710.09755

On the divisibility of class numbers of quadratic fields and the solvability of Diophantine equations

Azizul Hoque·Helen K. Saikia
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Abstract

In this paper we provide criteria for the insolvability of the Diophantine equation $x^2+D=y^n$. This result is then used to determine the class number of the quadratic field $\mathbb{Q}(\sqrt{-D})$. We also determine some criteria for the divisibility of the class number of the quadratic field $\mathbb{Q}(\sqrt{-D})$ and this result is then used to discuss the solvability of the Diophantine equation $x^2+D=y^n$.

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Azizul Hoque, Helen K. Saikia. 2017-10-26. On the divisibility of class numbers of quadratic fields and the solvability of Diophantine equations. https://doi.org/10.1007/s40324-016-0065-1

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