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 $k$.
Citation
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
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