Year: 2024
Type: article
Abstract: This study researches numbers that are powers of two and can be represented as the sum of the squares of any two Lucas numbers. We apply Baker's theory of linear forms in logarithms of algebraic numbers, combined with a variation of the Baker--Davenport reduction method, to solve the Diophantine equation $$L^2_m+L^2_n=2^a$$, where $$m$$, $$n$$ and $$a$$ are positive integers, as presented in this study.
Author: Ahmet Emin
Institution: Karabük University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4401993201