Simultaneous integer sequences and solving the pell equation
Küçük Resim Yok
Tarih
2016
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Jangjeon Mathematical Society
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Let k ? 1 be a fixed integer. In this work, we set two simultaneous integer sequences defined by Xn = (4k2 + 1)Xn-1 + (4k2 + 1)Xn-2 - Xn-3 and Yn = (4k2 + 1)Yn-1 + (4k2 + 1)Yn-2 - Yn-3 for n ? 3 with initial terms X0 = 1, X1 = 2k2 +1, X2 = 8k4 + 8k2 +1 and Y0 = 0, Y1 = 2k, Y2 = 8k3 + 4k and derived some algebraic identities on them. Further, we are able to determine all integer solutions of the Pell equation x2 - (k2 + 1)y2 = 1 as (xn,yn) = (Xn, Yn) for every n ? 1. © 2016, Jangjeon Mathematical Society. All rights reserved.
Açıklama
Anahtar Kelimeler
Binary linear recurrences; Continued fraction; Pell equation; Simultaneous integer sequences
Kaynak
Advanced Studies in Contemporary Mathematics (Kyungshang)
WoS Q Değeri
Scopus Q Değeri
N/A
Cilt
26
Sayı
2
