Solutions to $xyz = 1$ and $x + y + z = k$ in algebraic integers of small degree, II
Acta Arithmetica, Tome 171 (2015) no. 3, pp. 257-276
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let $k\in {\mathbb Z}$ be such that $|\mathcal E_k({\mathbb Q})|$ is finite, where $\mathcal E_k:\ y^2 = 1 - 2 k x + k^2 x^2 -4 x^3$. We complete the determination of all solutions to $xyz = 1$ and $x + y + z = k$ in integers of number fields of degree at most four over ${\mathbb Q}$.
Keywords:
mathbb mathcal mathbb finite where mathcal complete determination solutions xyz integers number fields degree mathbb
Affiliations des auteurs :
H. G. Grundman 1 ; L. L. Hall-Seelig 2
@article{10_4064_aa171_3_4,
author = {H. G. Grundman and L. L. Hall-Seelig},
title = {Solutions to $xyz = 1$ and $x + y + z = k$ in algebraic integers of small degree, {II}},
journal = {Acta Arithmetica},
pages = {257--276},
publisher = {mathdoc},
volume = {171},
number = {3},
year = {2015},
doi = {10.4064/aa171-3-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa171-3-4/}
}
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H. G. Grundman; L. L. Hall-Seelig. Solutions to $xyz = 1$ and $x + y + z = k$ in algebraic integers of small degree, II. Acta Arithmetica, Tome 171 (2015) no. 3, pp. 257-276. doi: 10.4064/aa171-3-4
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