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

2018/07/21 by Asim Patra, Patra, Asim
Engineering · Physics and Astronomy · #11B39 #Advanced Mathematical Theories and Applications #FOS: Mathematics #Number Theory (math.NT) #Sports Dynamics and Biomechanics

paper · pdf · doi:10.48550/arxiv.1807.10133

openalex publication_date 2018/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article the Diophantine equations of the form x²-8C_nxy+\n16y²=\±2^r, x⁴-8C_nx²y+ 16y²=\±2^r and\nx²-8C_nxy²+ 16y⁴=\±2^r are taken into consideration for the\ninvestigations of existence of any positive integer solutions. Furthermore, the\nsolutions are manifested in terms of the balancing, Pell and Lucas-Pell\nnumbers.\n

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