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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 장전수학회 Advanced Studies in Contemporary Mathematics Advanced Studies in Contemporary Mathematics Vol.26 No.2
- 발행연도
- 2016.1
- 수록면
- 263 - 274 (12page)
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초록· 키워드
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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.
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참고문헌 (10)
참고문헌 신청
E.J. Barbeau / 2003 / Pell's Equation / Springer-Verlag New York, Inc
J.H. Conway / 1996 / The Book of Numbers / Springer-Verlag
H.M. Edward / 1977 / Graduate Texts in Mathematics / Springer-Verlag
P. Hilton / 1997 / Mathematical Re ections in a Room with Many Mirrors / Springer-Verlag
M. Jacobson / 2010 / CMS Books in Mathematics / Springer
J.H. Conway / 1996 / The Book of Numbers / Springer-Verlag
H.M. Edward / 1977 / Graduate Texts in Mathematics / Springer-Verlag
P. Hilton / 1997 / Mathematical Re ections in a Room with Many Mirrors / Springer-Verlag
M. Jacobson / 2010 / CMS Books in Mathematics / Springer
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