Solutions to $xyz = 1$ and $x + y + z = k$ in algebraic integers of small degree, II
Volume 171 / 2015
Acta Arithmetica 171 (2015), 257-276
MSC: Primary 11D25; Secondary 11G05, 11R16.
DOI: 10.4064/aa171-3-4
Abstract
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 ${\mathbb Q}$.
