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