A. Patra

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math.NT2019

Appearance of Balancing and related number sequences in steady state probabilities of some Markov chains

Asim Patra, Gopal Krishna Panda

Balancing and Lucas-balancing numbers are solutions of a Diophantine equation and satisfy a second order homogeneous recurrence relation. Interestingly, these numbers can be seen a…

math.NT2018

Positive Integer Solutions of Certain Diophantine Equations Involving Lucas-Balancing numbers

Asim Patra

In this article the Diophantine equations of the form $x^{2} - 8 C_{n} x y + 16 y^{2} = \pm 2^{r}$ , $x^{4} - 8 C_{n} x^{2} y + 16 y^{2} = \pm 2^{r}$ and $x^{2} - 8 C_{n} x y^{2} + 16 y^{4} = \pm 2^{r}$ are take…