Solutions to $xyz = 1$ and $x+y+z = k$ in algebraic integers of small degree, I
Acta Arithmetica, Tome 162 (2014) no. 4, pp. 381-392
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 $|\mathcal E_k(\mathbb {Q})| = 3$, where $\mathcal E_k: y^2 = 1 - 2 k x + k^2 x^2 -4 x^3$. We determine 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 where mathcal determine solutions xyz integers number fields degree mathbb
Affiliations des auteurs :
H. G. Grundman 1 ; L. L. Hall-Seelig 2
@article{10_4064_aa162_4_5,
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, {I}},
journal = {Acta Arithmetica},
pages = {381--392},
publisher = {mathdoc},
volume = {162},
number = {4},
year = {2014},
doi = {10.4064/aa162-4-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa162-4-5/}
}
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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, I. Acta Arithmetica, Tome 162 (2014) no. 4, pp. 381-392. doi: 10.4064/aa162-4-5
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