Abstract
In this study, the diophantine equations \(x^2 -32B_nxy-32y^2 =\pm 32^{r}\), \(x^4 -32B_nxy-32y^2 =\pm 32^{r}\) and \(x^2 -32B_nxy-32y^4 =\pm 32^{r}\) are considered and determined when these equations have positive integer solutions. Moreover, all positive integer solutions of these diophantine equations in terms of balancing and Lucas-balancing numbers are also found out.
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Patel, B.K., Ray, P.K. & Sahukar, M.K. Positive integer solutions of certain diophantine equations. Proc Math Sci 128, 5 (2018). https://doi.org/10.1007/s12044-018-0377-4
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DOI: https://doi.org/10.1007/s12044-018-0377-4