Number Theory

    

On Conjectures About the Simultaneous Pell Equations X2−(a2−1)y2=1 and Y2−pz2=1

Authors: Michael C. I. Nwogugu

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, the Ai, Chen, Zhang & Hu (2015) Conjecture, the Yuan (2004) Conjecture, the Keskin, Karaatlı, et. al. (2017) Conjecture, the Cipu (2018) Conjecture, and the Cipu (2007) Conjecture [all of which pertain to the system of Simultaneous Pell equations x^2−(a^2−1)y^2=1 and y^2−pz^2=1] are wrong or incomplete (incomplete in the sense that they didn’t provide complete solutions for the system of equations). This article also introduces simple Java codes for solutions to this class of equations for positive-integers up to (10)^2457600000 (and even greater positive-integers depending on available computing power).

Comments: 10 Pages. The copyright license-type for this article is CC-BY-NC-ND

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Submission history

[v1] 2022-08-09 00:43:37

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