Work

Nonnegative integer solutions of the equation L (k) n - L (k) m = 2 · 3a

Year: 2025

Type: article

Abstract: For an integer k ≥ 2, let (L (k) n )n≥−(k−2) be the k-generalized Lucas sequence, which starts with 0, ..., 0, 2, 1 (k terms) and each term afterwards is the sum of the k preceding terms. In 2019, Bitim found all the solutions of the Diophantine equation Ln − Lm = 2 · 3 a . In this paper, we generalize this result by considering the k-generalized Lucas sequence, i.e., we solve the Diophantine equation L (k) n − L (k) m = 2 · 3 a in positive integers n, m, a with k ≥ 3. To obtain our main result, we use Baker’s method and the Baker-Davenport reduction method.

Source: Mathematical communications

DOI: 10.64785/mc.30.1.7

Authors: Bakr Kouroumane Rihane, Alain Togbe, Salah Eddine Rihane, Alain Togbe

Institutions: Gamal Abdel Nasser University of Conakry, National Higher School of Mathematics, Purdue University Northwest

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4413993798

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