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On the Positive Pell Equation

Author: J.Shanthi and K.B.Abirami

Published On: 2024-10-23

Abstract

   A binary quadratic equation of the form where D is non-square positive integer has been study by various mathematicians for it non-trivial integral solutions when D takes different integral values. The binary quadratic Diophantine equation represented by the positive pellian  is analysed for its non-zero distinct solutions. A few interesting relations among the solutions are given. Further, employing the solutions of the above hyperbola, the solutions of other choices of hyperbolas and parabolas are obtained.

KEYWORDS:

       Binary quadratic, Hyperbola, Parabola, Pell equation, Integral solutions. 

Keywords
       Binary quadratic Hyperbola Parabola Pell equation Integral solutions. 
Article Information
Volume

7

Year

2024

Review Rounds

1

Article Type

Research Article

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