Tokyo Journal of Mathematics

The Diophantine Equation $X^3=u+27v$ over Real Quadratic Fields

Takaaki KAGAWA

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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 $k$.

Article information

Source
Tokyo J. Math., Volume 33, Number 1 (2010), 159-163.

Dates
First available in Project Euclid: 21 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1279719584

Digital Object Identifier
doi:10.3836/tjm/1279719584

Mathematical Reviews number (MathSciNet)
MR2682887

Zentralblatt MATH identifier
1227.11052

Subjects
Primary: 11D99: None of the above, but in this section
Secondary: 11G05: Elliptic curves over global fields [See also 14H52]

Citation

KAGAWA, Takaaki. The Diophantine Equation $X^3=u+27v$ over Real Quadratic Fields. Tokyo J. Math. 33 (2010), no. 1, 159--163. doi:10.3836/tjm/1279719584. https://projecteuclid.org/euclid.tjm/1279719584


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References

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