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June 2010 The Diophantine Equation $X^3=u+27v$ over Real Quadratic Fields
Takaaki KAGAWA
Tokyo J. Math. 33(1): 159-163 (June 2010). DOI: 10.3836/tjm/1279719584

Abstract

Let $k$ be a real quadratic field.The Diophantine equation $X^3=u+27v$ in $X\in\mathcal{O}_k$ (the ring of integers of $k$),$u,v\in\mathcal{O}_k^\times$ (the group of units of $k$) is solved under some assumptions on $k$.

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Takaaki KAGAWA. "The Diophantine Equation $X^3=u+27v$ over Real Quadratic Fields." Tokyo J. Math. 33 (1) 159 - 163, June 2010. https://doi.org/10.3836/tjm/1279719584

Information

Published: June 2010
First available in Project Euclid: 21 July 2010

zbMATH: 1227.11052
MathSciNet: MR2682887
Digital Object Identifier: 10.3836/tjm/1279719584

Subjects:
Primary: 11D99
Secondary: 11G05

Rights: Copyright © 2010 Publication Committee for the Tokyo Journal of Mathematics

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Vol.33 • No. 1 • June 2010
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