Abstract
The binary quadratic equation represented by the positive pellian Y2 = 72X2 + 36 is analysed for its distinct integer solutions. A few interesting relations among the solutions are given. Further, employing the solutions of the above hyperbola, we have obtained solutions of other choices of hyperbolas, parabolas and special Pythagorean triangle.
Highlights
Cite This Article: M.A.Gopalan, A.Kavitha, and A.Jesintha Mary
We observe some interesting relations among the solutions which are presented below: 1) xn and yn values are always even
Employing linear combinations among the solutions of (1), one may generate integer solutions for other choices of hyperbola which are presented in the Table 2 below: Table 2: Hyperbolas
Summary
Cite This Article: M.A.Gopalan, A.Kavitha, and A.Jesintha Mary. “ON THE POSITIVE PELL EQUATION Y2 = 72X2 + 36.” International Journal of Research - Granthaalayah, 5(7:SE), 68-74. 1. Introduction The binary quadratic equation of the form y2 Dx2 1 where D is non-square positive integer has been studied by various mathematicians for its non-trivial integral solutions when D takes different values [1,2,3,4]. In this communication, yet another interesting hyperbola given by y2 72x2 36 is considered and infinitely many integer solutions are obtained.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
