A note on the Diophantine equation $(x^2-1)(y^2-1)=(z^2-1)^2$
Volume 124 / 2021
Banach Center Publications 124 (2021), 23-26
MSC: 11D25, 11G05.
DOI: 10.4064/bc124-2
Abstract
In this note we investigate the equation in the title from the point of view of arithmetic geometry and we show that it defines — up to a trivial factor — an elliptic surface; then we place in this context the main result on integer solutions to the equation obtained by Schinzel and Sierpiński.
