Intrinsic Solutions of the Pell Equation \(\mathit{x}^2\) = 5\(\mathit{y}^2\) + 9\(^\mathit{t}\)

Authors

  • S. Vidhya PG & Research Department of Mathematics, Cauvery College for Women (Autonomous), Tiruchirappalli – 620 018, Tamil Nadu, India.
  • G. Janaki PG & Research Department of Mathematics, Cauvery College for Women (Autonomous), Tiruchirappalli – 620 018, Tamil Nadu, India.
  • B. Amala PG & Research Department of Mathematics, Cauvery College for Women (Autonomous), Tiruchirappalli – 620 018, Tamil Nadu, India.

DOI:

https://doi.org/10.9734/bpi/mono/978-81-967488-3-8/CH3

Keywords:

Pell equation, Diophantine equation, integer solutions

Abstract

We search for a non-trivial integer solutions to the equation \(\mathit{x}^2\) = 5\(\mathit{y}^2\) + 9\(^\mathit{t}\) , \(\mathit{t}\) \(\in\) \(\mathit{N}\) , where i) t = 2k+1, ii) t = 2k for all \(\mathit{k}\) \(\in\) \(\mathit{N}\) , Additionally the recurrence relation for the solutions are also discovered.

Published

2023-11-11

How to Cite

S. Vidhya, G. Janaki, & B. Amala. (2023). Intrinsic Solutions of the Pell Equation \(\mathit{x}^2\) = 5\(\mathit{y}^2\) + 9\(^\mathit{t}\). Explorations in Diophantine Equations, 22–27. https://doi.org/10.9734/bpi/mono/978-81-967488-3-8/CH3

Issue

Explorations in Diophantine Equations

Section

Contents