Geodesic
Solutions to $xyz = 1$ and $x+y+z = k$ in algebraic integers of small degree, I
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.
Acta Arithmetica, Tome 162 (2014) no. 4, pp. 381-392 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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. 
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     title = {Solutions to $xyz = 1$ and $x+y+z = k$ in algebraic integers of small degree, {I}},
     journal = {Acta Arithmetica},
     pages = {381--392},
     year = {2014},
     volume = {162},
     number = {4},
     doi = {10.4064/aa162-4-5},
     language = {en},
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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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