On the system of Pell equations $$x^2-(a^2b^2 {\pm } a)y^2=1$$ x 2 - ( a 2 b 2 ± a ) y 2 = 1 and $$y^2-pz^2=4b^2$$ y 2 - p z 2 = 4 b 2

Salah E. Rihane (), Euloge B. Tchammou () and Alain Togbé ()
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Salah E. Rihane: Université des Sciences et de la Technologie Houari-Boumediène (USTHB)
Euloge B. Tchammou: Université d’Abomey-Cavali
Alain Togbé: Purdue University Northwest

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 1, 224-230

Abstract: Abstract In this paper, we consider the title simultaneous Pell equations, where $$a\ge 2,b \ge 1$$ a ≥ 2 , b ≥ 1 are positive integers and p is an odd prime. Particularly, we give all the solutions when $$2\le a\le 1000$$ 2 ≤ a ≤ 1000 and $$1\le b\le 1000$$ 1 ≤ b ≤ 1000 .

Keywords: Pell equations; Simultaneous Pell equations; 11D09 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00080-1

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