This paper is published in Volume-7, Issue-3, 2021
Area
Number Theory
Author
M. A. Gopalan, A. Vijayasankar, Sharadha Kumar
Org/Univ
Shrimati Indira Gandhi College, Tiruchirappalli, Tamil Nadu, India
Pub. Date
15 May, 2021
Paper ID
V7I3-1296
Publisher
Keywords
Positive Pell Equation, Binary Quadratic, Hyperbola, Parabola, 2^Nd Order Ramanujan Numbers, Sequence Of Diophantine 3-Tuples

Citationsacebook

IEEE
M. A. Gopalan, A. Vijayasankar, Sharadha Kumar. Observations on the Pell Equation x2=3(y2+y)+1, International Journal of Advance Research, Ideas and Innovations in Technology, www.IJARIIT.com.

APA
M. A. Gopalan, A. Vijayasankar, Sharadha Kumar (2021). Observations on the Pell Equation x2=3(y2+y)+1. International Journal of Advance Research, Ideas and Innovations in Technology, 7(3) www.IJARIIT.com.

MLA
M. A. Gopalan, A. Vijayasankar, Sharadha Kumar. "Observations on the Pell Equation x2=3(y2+y)+1." International Journal of Advance Research, Ideas and Innovations in Technology 7.3 (2021). www.IJARIIT.com.

Abstract

This paper concerns with the problem of obtaining non-zero distinct integer solutions to the positive pell equation represented by the binary quadratic equation x^2=3(y^2+y)+1. A few interesting relations among the solutions are presented. Further, by considering suitable linear combinations among the solutions of the considered hyperbola, the other choices of hyperbolas, parabolas, order Ramanujan numbers, sequence of diophantine 3-tuples with the suitable property are presented. A general formula for generating a sequence of integer solutions based on the given solution is illustrated.
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