Geodesic
Solutions to $xyz = 1$ and $x+y+z = k$ in algebraic integers of small degree, I
H. G. Grundman1 ; L. L. Hall-Seelig2
1 Department of Mathematics Bryn Mawr College Bryn Mawr, PA 19010, U.S.A.
2 Department of Mathematics Merrimack College North Andover, MA 01845, U.S.A.
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 $\mathbb {Q}$.
DOI : 10.4064/aa162-4-5
Keywords: mathbb mathcal mathbb where mathcal determine solutions xyz integers number fields degree mathbb

H. G. Grundman 1 ; L. L. Hall-Seelig 2

1 Department of Mathematics Bryn Mawr College Bryn Mawr, PA 19010, U.S.A.
2 Department of Mathematics Merrimack College North Andover, MA 01845, U.S.A. 
@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/}
}
TY  - JOUR
AU  - H. G. Grundman
AU  - L. L. Hall-Seelig
TI  - Solutions to $xyz = 1$ and $x+y+z = k$ in algebraic integers of small degree, I
JO  - Acta Arithmetica
PY  - 2014
SP  - 381
EP  - 392
VL  - 162
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa162-4-5/
DO  - 10.4064/aa162-4-5
LA  - en
ID  - 10_4064_aa162_4_5
ER  - 
%0 Journal Article
%A H. G. Grundman
%A L. L. Hall-Seelig
%T Solutions to $xyz = 1$ and $x+y+z = k$ in algebraic integers of small degree, I
%J Acta Arithmetica
%D 2014
%P 381-392
%V 162
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa162-4-5/
%R 10.4064/aa162-4-5
%G en
%F 10_4064_aa162_4_5
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. http://geodesic.mathdoc.fr/articles/10.4064/aa162-4-5/

Cité par Sources :