Solutions to and x + y + z = k in algebraic integers of small degree, II
Tom 171 / 2015
Acta Arithmetica 171 (2015), 257-276
MSC: Primary 11D25; Secondary 11G05, 11R16.
DOI: 10.4064/aa171-3-4
Streszczenie
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}.
