Year: 2025
Type: article
Abstract: Let k and p be prime numbers with p>2. In this note, we find all positive integer solutions to the Diophantine equations x^2-kxy-y^2=±k, x^2-(k^2+4) y^2=±4k, x^2-2pxy-y^2=±2p, x^2-kxy-y^2=±k(k^2+4) in terms of generalized Fibonacci and Lucas numbers.
Authors: Refik Keskin, Kübra Ged, Fatih Erduvan
Institution: Sakarya University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4407125528