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

Volume 59 / 2011

Takaaki Kagawa Bulletin Polish Acad. Sci. Math. 59 (2011), 1-9 MSC: 11D99, 11G05. DOI: 10.4064/ba59-1-1


Let $k$ be a real quadratic field and let $\mathcal O_k$ and $\mathcal O_k^\times$ be the ring of integers and the group of units, respectively. A method of solving the Diophantine equation $X^3=u+v$ ($X\in\mathcal O_k$, $u,v\in\mathcal O_k^{\times}$) is developed.


  • Takaaki KagawaDepartment of Mathematical Sciences
    Ritsumeikan University
    Kusatsu, Shiga 525-8577, Japan

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