ON THE SYSTEM OF DIOPHANTINE EQUATIONS x² − 7y² = 1 AND x = az² − b 


By

Radhika Das¹, Manju Somanath² and V. A. Bindu³

Department of Mathematics 

¹,³Rajagiri School of Engineering & Technology, Kakkanad, Cochin, Kerala, India-682039 

(Research Scholar, National College, Autonomous, Affiliated to Bharathidasan University, Trichy, Tamil Nadu, India-620001) 

²National College,Autonomous, Affiliated to Bharathidasan University, Trichy, Tamil Nadu, India-620001 

Email: krishnagangaradhi@gmail.com, manjuajil@yahoo.com, binduabhilash@gmail.com 

(Received: July 16, 2023; In format: September 09, 2023; Revised: April 25, 2024; Accepted: April 27, 2024) 


DOI: https://doi.org/10.58250/jnanabha.2024.54132



Abstract

The quartic model of an elliptic curve represented by the system of Diophantine equations x²−7y² = 1 and x = az² − b , where a and b are integers, will be examined for integral solutions. In this work, the system of equations is solved using the algebraic number theory method. Solving a system of equations using the parameters 1 ≤ a ≤ 10 and 1 < b < 11 is an application. 


2010 Mathematics Subject Classification: 11D09. 

Keywords and Phrases: Pell equation, Integer Solutions, Diophantine equations, Algebraic Number Theory, Recurrence Relation. 

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