The Diophantine Equation $X^3=u+v$ over
Real Quadratic Fields
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) no. 1, pp. 1-9
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
real quadratic field mathcal mathcal times ring integers group units respectively method solving diophantine equation mathcal mathcal times developed
Affiliations des auteurs :
Takaaki Kagawa 1
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author = {Takaaki Kagawa},
title = {The {Diophantine} {Equation} $X^3=u+v$ {over
Real} {Quadratic} {Fields}},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
pages = {1--9},
publisher = {mathdoc},
volume = {59},
number = {1},
year = {2011},
doi = {10.4064/ba59-1-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba59-1-1/}
}
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Takaaki Kagawa. The Diophantine Equation $X^3=u+v$ over Real Quadratic Fields. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) no. 1, pp. 1-9. doi: 10.4064/ba59-1-1
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