Integral Solutions of the Binary Quadratic Diophantine Equation x\({^2}\) - 2xy -y\({^2}\) + 2x +14y= 72

C.  Saranya; G.  Janaki

doi:10.9734/bpi/ramrcs/v2/13036D

Integral Solutions of the Binary Quadratic Diophantine Equation x\({^2}\) - 2xy -y\({^2}\) + 2x +14y= 72

Authors

C. Saranya Department of Mathematics, Cauvery College for Women (Autonomous), (Affiliated to Bharathidasan University), Tiruchirappalli, Taminadu, India.
G. Janaki Department of Mathematics, Cauvery College for Women (Autonomous), (Affiliated to Bharathidasan University), Tiruchirappalli, Taminadu, India.

DOI:

https://doi.org/10.9734/bpi/ramrcs/v2/13036D

Keywords:

Binary quadratic equation, diophantine equation, integral solutions, hyperbola, parabola and pell equation

Abstract

In this chapter, the binary quadratic equation x² - 2xy - y² + 2x + 14y = 72 represents a hyperbola is analyzed for its non-zero distinct integer solutions. Also, we obtain a sequence of its integral solutions and present a few interesting relations among them. The recurrence relations satisfied by the solutions x and y are obtained.

Published

2021-10-27

How to Cite

C. Saranya, & G. Janaki. (2021). Integral Solutions of the Binary Quadratic Diophantine Equation x\({^2}\) - 2xy -y\({^2}\) + 2x +14y= 72. Recent Advances in Mathematical Research and Computer Science Vol. 2, 83–90. https://doi.org/10.9734/bpi/ramrcs/v2/13036D

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Issue

Recent Advances in Mathematical Research and Computer Science Vol. 2

Section

Chapters