Abstract
In this study, we determine when the Diophantine equation x 2−kxy+y 2−2n = 0 has an infinite number of positive integer solutions x and y for 0 ⩽ n ⩽ 10. Moreover, we give all positive integer solutions of the same equation for 0 ⩽ n ⩽ 10 in terms of generalized Fibonacci sequence. Lastly, we formulate a conjecture related to the Diophantine equation x 2 − kxy + y 2 − 2n = 0.
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Keskin, R., Şiar, Z. & Karaatli, O. On the Diophantine equation x 2 − kxy + y 2 − 2n = 0. Czech Math J 63, 783–797 (2013). https://doi.org/10.1007/s10587-013-0052-y
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DOI: https://doi.org/10.1007/s10587-013-0052-y