On Positive Integer Solutions of a Special Diophantine Equation
Yazarlar (1)
Doç. Dr. Ahmet EMİN Karabük Üniversitesi, Türkiye
| Makale Türü | Özgün Makale (SCOPUS dergilerinde yayınlanan tam makale) | ||
| Dergi Adı | Palestine Journal of Mathematics | ||
| Dergi ISSN | 2219-5688 Dergi Bilgileri (2024) | ||
| Dergi Tarandığı Indeksler | Scopus | ||
| Makale Dili | İngilizce | Basım Tarihi | 12-2024 |
| Cilt / Sayı / Sayfa | 13 / 4 / 1266–1276 | DOI | – |
| Makale Linki | https://pjm.ppu.edu/sites/default/files/papers/PJM_13%284%29_2024_1266_to_1276.pdf | ||
| UAK Araştırma Alanları |
Cebir ve Sayılar Teorisi
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| Özet |
| In this study, the positive solutions of the Diophantine equation D: x2−(σ2+ 4) y2−(2σ− 2) x−(2σ4+ 8σ2) y− σ6− 4σ4+ σ2− 2σ− 3= 0 on the set Z are investigated, along with some recurrence relations that provide the relationships among these solutions. In addition, solutions of the Diophantine equation D in terms of generalized Fibonacci and Lucas sequences are examined. Furthermore, we search for the solutions of this equation over finite fields Fp where p is prime and p> 5. Finally, an example is given that satisfies our results. |
| Anahtar Kelimeler |
| Diophantine equation | generalized Fibonacci and Lucas sequences | Pell equation | recurrence relation |
