On solutions of some Diophantine equations

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.

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Publication Details

Journal
GAZI UNIVERSITY JOURNAL OF SCIENCE
Published
2025-02-04
DOI
https://doi.org/10.35378/gujs.1378010
Primary Topic
Advanced Mathematical Theories and Applications
Type
article
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article

On solutions of some Diophantine equations

Fatih Erduvan, Refık Keskin, Kübra Ged
GAZI UNIVERSITY JOURNAL OF SCIENCE
Advanced Mathematical Theories and Applications
article

On solutions of some Diophantine equations

Fatih Erduvan, Refık Keskin, Kübra Ged
article en

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.

GAZI UNIVERSITY JOURNAL OF SCIENCEVol. 38(2)
Sakarya University (TR)
Openalex Percentile: Top 98%
Advanced Mathematical Theories and Applications
DOIOpen Access PDFOpenAlex
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On solutions of some Diophantine equations — Fatih Erduvan, Refık Keskin, et al. · GAZI UNIVERSITY JOURNAL OF SCIENCE (2025) | TGRS Research Map | TGRS