On positive integer solutions of a special diophantine equation
Küçük Resim Yok
Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Palestine Polytechnic University
Erişim Hakkı
info:eu-repo/semantics/openAccess
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.
Açıklama
Anahtar Kelimeler
Diophantine equation, generalized Fibonacci and Lucas sequences, Pell equation, recurrence relation
Kaynak
Palestine Journal of Mathematics
WoS Q Değeri
Scopus Q Değeri
Q4
Cilt
13
Sayı
4
