On Conjectures About The Simultaneous Pell Equations x2−(a2−1)y2=1 and y2−pz2=1.

Abstract

This article shows that the Qu (2018) conjectures, the Yang & Fu (2018) conjectures, the Jiang (2020) Conjecture-#1, the Tao (2016) Conjecture-#1, the Cipu & Mignotte (2007) Conjecture and the Cipu (2007) Conjecture [all of which pertain to the system of Simultaneous Pell equations x2−(a2−1)y2=1 and y2−pz2=1] are wrong.