Solutions to xyz = 1 and x+y+z = k in algebraic integers of small degree, I

H. G. Grundman, and L. L. Hall-Seelig. "Solutions to xyz = 1 and x+y+z = k in algebraic integers of small degree, I." Acta Arithmetica 162.4 (2014): 381-392. <http://eudml.org/doc/279779>.

@article{H2014,
abstract = {Let k ∈ ℤ be such that $|_k(ℚ )| = 3$, where $_k: y² = 1 - 2kx + k²x² - 4x³$. We determine all solutions to xyz = 1 and x + y + z = k in integers of number fields of degree at most four over ℚ.},
author = {H. G. Grundman, L. L. Hall-Seelig},
journal = {Acta Arithmetica},
keywords = {diophantine equations; units},
language = {eng},
number = {4},
pages = {381-392},
title = {Solutions to xyz = 1 and x+y+z = k in algebraic integers of small degree, I},
url = {http://eudml.org/doc/279779},
volume = {162},
year = {2014},
}

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
VL - 162
IS - 4
SP - 381
EP - 392
AB - Let k ∈ ℤ be such that $|_k(ℚ )| = 3$, where $_k: y² = 1 - 2kx + k²x² - 4x³$. We determine all solutions to xyz = 1 and x + y + z = k in integers of number fields of degree at most four over ℚ.
LA - eng
KW - diophantine equations; units
UR - http://eudml.org/doc/279779
ER -