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

  • Authors

    • M.A. Gopalan Professor,Dept. of Mathematics, Srimathi Indira Gandhi College, Trichy-620002
    • V. Sangeetha Assistant Professor,Dept. of Mathematics, National College, Trichy-620001
    • Manju Somanath Assistant Professor,Dept. of Mathematics, National College, Trichy-620001
    2014-02-11
    https://doi.org/10.14419/ijamr.v3i1.1701

  • Abstract

    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 are obtained.

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

  • References

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  • How to Cite

    Gopalan, M., Sangeetha, V., & Somanath, M. (2014). On the integer solutions of the Pell equation \(x^2=13y^2-3^t\). International Journal of Applied Mathematical Research, 3(1), 58-61. https://doi.org/10.14419/ijamr.v3i1.1701

    Received date: 2014-01-01

    Accepted date: 2014-01-24

    Published date: 2014-02-11