On the Diophantine equation x2 - kxy + y2 - 2n = 0
Czechoslovak Mathematical Journal, cilt.63, sa.3, ss.783-797, 2013 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 63 Sayı: 3
- Basım Tarihi: 2013
- Doi Numarası: 10.1007/s10587-013-0052-y
- Dergi Adı: Czechoslovak Mathematical Journal
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.783-797
- Anahtar Kelimeler: Diophantine equation, generalized Fibonacci number, generalized Lucas number, Pell equation
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Bilecik Şeyh Edebali Üniversitesi Adresli: Evet
Özet
In this study, we determine when the Diophantine equation x 2-kxy+y 2-2n = 0 has an infinite number of positive integer solutions x and y for 0 ≤ n ≤ 10. Moreover, we give all positive integer solutions of the same equation for 0 ≤ n ≤ 10 in terms of generalized Fibonacci sequence. Lastly, we formulate a conjecture related to the Diophantine equation x 2 - kxy + y 2 - 2n = 0. © 2013 Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic.