Solutions of the Diophantine Equations Br=Js+Jt and Cr=Js+Jt

Ahmed Gaber, Mohiedeen Ahmed and Xiaogang Liu

Journal of Mathematics, 2023, vol. 2023, 1-8

Abstract: Let Brr≥0, Jrr≥0, and Crr≥0 be the balancing, Jacobsthal, and Lucas balancing numbers, respectively. In this paper, the diophantine equations Br=Js+Jt and Cr=Js+Jt are completely solved. The solutions rely basically on Matveev’s theorem on linear forms in logarithms of algebraic numbers and a procedure of reducing the upper bound due to Dujella and Pethö.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8851478

DOI: 10.1155/2023/8851478

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