# On the integer solutions of the Pell equation \(x^2=13y^2-3^t\)

## DOI:

https://doi.org/10.14419/ijamr.v3i1.1701## Published:

2014-02-11## Abstract

The binary quadratic Diophantine equation represented by is considered and analyzed for its non-zero distinct integer solutions for the choices of *t*Â 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 are obtained.

**Keywords**: Pell equation, integer solutions of Pell equation, binary quadratic Diophantine equation.

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