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GENERALIZED FIBONACCI AND LUCAS NUMBERS OF THE FORM wx2 AND wx2 ∓ 1
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 Title & Authors
GENERALIZED FIBONACCI AND LUCAS NUMBERS OF THE FORM wx2 AND wx2 ∓ 1
Keskin, Refik;
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 Abstract
Let be an integer and let () and () denote generalized Fibonacci and Lucas sequences defined by $U_0
 Keywords
generalized Fibonacci numbers;generalized Lucas numbers;congruences;Diophantine equation;
 Language
English
 Cited by
1.
GENERALIZED LUCAS NUMBERS OF THE FORM 5kx2 AND 7kx2,;;

대한수학회보, 2015. vol.52. 5, pp.1467-1480 crossref(new window)
1.
On the equation V n = w x 2 ∓ 1, Arab Journal of Mathematical Sciences, 2017, 23, 2, 148  crossref(new windwow)
2.
GENERALIZED LUCAS NUMBERS OF THE FORM 5kx2AND 7kx2, Bulletin of the Korean Mathematical Society, 2015, 52, 5, 1467  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)
4.
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)
 References
1.
R. T. Bumby, The diophantine equation $3x^4-2y^2=1$, Math. Scand. 21 (1967), 144-148.

2.
J. H. E. Cohn, Squares in some recurrent sequences, Pacific J. Math. 41 (1972), 631-646. crossref(new window)

3.
J. P. Jones, Representation of solutions of Pell equations using Lucas sequences, Acta Academia Pead. Agr., Sectio Mathematicae 30 (2003), 75-86.

4.
D. Kalman and R. Mena, The Fibonacci numbersexposed, Math. Mag. 76 (2003), no. 3, 167-181. crossref(new window)

5.
R. Keskin, Solutions of some quadratics diophantine equations, Comput. Math. Appl. 60 (2010), no. 8, 2225-2230. crossref(new window)

6.
R. Keskin and Z. Siar, Positive integer solutions of some diophantine equations in terms of integer sequences (submitted).

7.
W. L.McDaniel, The g.c.d. in Lucas sequences and Lehmer number sequences, Fibonacci Quart. 29 (1991), no. 1, 24-30.

8.
W. L.McDaniel, Diophantine representation of Lucas sequences, Fibonacci Quart. 33 (1995), no. 1, 58-63.

9.
R. Melham, Conics which characterize certain Lucas sequences, Fibonacci Quart. 35 (1997), no. 3, 248-251.

10.
J. B. Muskat, Generalized Fibonacci and Lucas sequences and rootfinding methods, Math. Comp. 61 (1993), no. 203, 365-372. crossref(new window)

11.
S. Rabinowitz, Algorithmic manipulation of Fibonacci identities, Applications of Fi-bonacci numbers, Vol. 6 (Pullman, WA, 1994), 389-408, Kluwer Acad. Publ., Dordrecht, 1996.

12.
P. Ribenboim, My Numbers, My Friends, Springer-Verlag New York, Inc., 2000.

13.
P. Ribenboim and W. L. McDaniel, The square terms in Lucas sequences, J. Number Theory 58 (1996), no. 1, 104-123. crossref(new window)

14.
P. Ribenboim and W. L. McDaniel, Squares in Lucas sequences having an even first parameter, Colloq. Math. 78 (1998), no. 1, 29-34.

15.
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, de Gruyter, Berlin, 2001.

16.
Z. Siar and R. Keskin, Some new identities concerning generalized Fibonacci and Lucas numbers, Hacet. J. Math. Stat. 42 (2013), no. 3, 211-222.

17.
Z. Siar and R. Keskin, The square terms in generalized Lucas sequence, Mathematika 60 (2014), 85-100. crossref(new window)