JOURNAL BROWSE
Search
Advanced SearchSearch Tips
GENERALIZED LUCAS NUMBERS OF THE FORM 5kx2 AND 7kx2
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
GENERALIZED LUCAS NUMBERS OF THE FORM 5kx2 AND 7kx2
KARAATLI, OLCAY; KESKIN, REFIK;
  PDF(new window)
 Abstract
Generalized Fibonacci and Lucas sequences () and () are defined by the recurrence relations $U_{n+1}
 Keywords
generalized Fibonacci numbers;generalized Lucas numbers;congruences;
 Language
English
 Cited by
1.
On the Lucas sequence equations $$V_{n}(P,1)=wkx^{2},$$ V n ( P , 1 ) = w k x 2 , $$w\in \left\{ 5,7\right\} $$ w ∈ 5 , 7, Periodica Mathematica Hungarica, 2016, 73, 1, 73  crossref(new windwow)
2.
On the equation V n = w x 2 ∓ 1, Arab Journal of Mathematical Sciences, 2017, 23, 2, 148  crossref(new windwow)
3.
Generalized Fibonacci numbers of the form $$wx^{2}+1$$ w x 2 + 1, Periodica Mathematica Hungarica, 2016, 73, 2, 165  crossref(new windwow)
 References
1.
J. H. E. Cohn, Squares in some recurrent sequences, Pacific J. Math. 41 (1972), 631-646. crossref(new window)

2.
B. Demirturk and R. Keskin, Integer solutions of some Diophantine equations via Fibonacci and Lucas numbers, J. Integer Seq. 12 (2009), no. 8, Article 09.8.7, 14 pp.

3.
D. Kalman and R. Mena, The Fibonacci numbers-exposed, Math. Mag. 76 (2003), no. 3, 167-181. crossref(new window)

4.
R. Keskin, Generalized Fibonacci and Lucas numbers of the form $wx^2$ and $wx^2$ ${\pm}$ 1, Bull. Korean Math. Soc. 51 (2014), no. 4, 1041-1054. crossref(new window)

5.
R. Keskin and O. Karaatli, Generalized Fibonacci and Lucas numbers of the form $5x^2$, Int. J. Number Theory 11 (2015), no. 3, 931-944. crossref(new window)

6.
W. L. McDaniel, Diophantine Representation of Lucas Sequences, Fibonacci Quart. 33 (1995), no. 1, 59-63.

7.
R. Melham, Conics which characterize certain Lucas sequences, Fibonacci Quart. 35 (1997), no. 3, 248-251.

8.
J. B. Muskat, Generalized Fibonacci and Lucas sequences and rootfinding methods, Math. Comp. 61 (1993), no. 203, 365-372. crossref(new window)

9.
S. Rabinowitz, Algorithmic manipulation of Fibonacci identities, Appl. Fibonacci Numbers 6 (1996), 389-408.

10.
P. Ribenboim, My Numbers, My Friends, Springer-Verlag New York, Inc., 2000.

11.
P. Ribenboim and W. L. McDaniel, The square terms in Lucas sequences, J. Number Theory 58 (1996), no. 1, 104-123. crossref(new window)

12.
P. Ribenboim and W. L. McDaniel, On Lucas sequence terms of the form $kx^2$, Number Theory: Proceedings of the Turku symposium on Number Theory in memory of Kustaa Inkeri (Turku, 1999), 293-303, Walter de Gruyter, Berlin, 2001.

13.
Z. Siar and R. Keskin, Some new identities concerning generalized Fibonacci and Lucas numbers, Hacet. J. Math. Stat. 42 (2013), no. 3, 211-222.

14.
Z. Siar and R. Keskin, The square terms in generalized Fibonacci sequence, Mathematika 60 (2014), no. 1, 85-100. crossref(new window)