A note on pencils of norm-form equations
Volume 203 / 2022
Acta Arithmetica 203 (2022), 19-26
MSC: Primary 11D57; Secondary 11D61, 11J86, 11R16.
DOI: 10.4064/aa210329-13-12
Published online: 18 March 2022
Abstract
We find all solutions to the parametrized family of norm-form equations $$ x^3-(t^3-1)y^3+3(t^3-1)xy+(t^3-1)^2 = \pm 1, $$ where $t \gt 1$ is an integer, studied by Amoroso, Masser and Zannier. Our proof relies upon an appeal to lower bounds for linear forms in logarithms and various elementary arguments.
