Geodesic
On Fibonacci and Lucas numbers of the form \(cx^2\)
Journal of integer sequences, Tome 14 (2011) no. 9
In this paper, by using some congruences concerning with Fibonacci and Lucas numbers, we completely solve the Diophantine equations $L_{n} = 2L_{m}x^{2}, F_{n} = 2F_{m}x^{2}, L_{n} = 6L_{m}x^{2}, F_{n} = 3F_{m}x^{2}$, and $F_{n} = 6F_{m}x^{2}$.
Classification : 11B37, 11B39
Keywords: Fibonacci numbers, Lucas numbers, congruences 
@article{JIS_2011__14_9_a4,
     author = {Keskin,  Refik and Yosma,  Zafer},
     title = {On {Fibonacci} and {Lucas} numbers of the form \(cx^2\)},
     journal = {Journal of integer sequences},
     year = {2011},
     volume = {14},
     number = {9},
     zbl = {1258.11017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_9_a4/}
}
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Keskin,  Refik; Yosma,  Zafer. On Fibonacci and Lucas numbers of the form \(cx^2\). Journal of integer sequences, Tome 14 (2011) no. 9. http://geodesic.mathdoc.fr/item/JIS_2011__14_9_a4/