On the integer solutions of the Pell equation x^2=13y^2-3^t
On the integer solutions of the Pell equation x^2=13y^2-3^t
The binary quadratic Diophantine equation represented by is considered and analyzed for its non-zero distinct integer solutions for the choices of t given by (i) \(t=1\) (ii) \(t=3\) (iii) \(t=5\) (iv) \(t=2k\) and (v) \(t=2k+5\). A few interesting relations among the solutions are presented. Further, recurrence relations on the solutions …