Upper bounds for the number of solutions for the Diophantine equation $y^{2}=px( Ax^{2}-C) $ $(C=2,\pm 1,\pm 4) $
Volume 159 / 2020
Colloquium Mathematicum 159 (2020), 243-257
MSC: Primary 11D25; Secondary 11B39.
DOI: 10.4064/cm7704-3-2019
Published online: 25 November 2019
Abstract
The purpose of this paper is to give new upper bounds for the number of positive solutions for the Diophantine equation $y^{2}=px(Ax^{2}-C)$, where $C\in \{2,\pm 1,\pm 4\}$, $p$ is an odd prime and $A$ is a positive integer.
