Geodesic
Integer solutions of some Diophantine equations via Fibonacci and Lucas numbers
Journal of integer sequences, Tome 12 (2009) no. 8
We study the problem of finding all integer solutions of the Diophantine equations $x^{2}-5F_{n}xy-5\left( -1\right) ^{n}y^{2}=\pm L_{n}^{2},x^{2}-L_{n}xy+\left( -1\right) ^{n}y^{2}=\pm 5F_{n}^{2},$ and $\% x^{2}-L_{n}xy+\left( -1\right) ^{n}y^{2}=\pm F_{n}^{2}.$ Using these equations, we also explore all integer solutions of some other Diophantine equations.
Classification : 11B37, 11B39, 11B50
Keywords: Fibonacci number, Lucas number, Diophantine equation 
@article{JIS_2009__12_8_a1,
     author = {Demirt\"urk,  Bahar and Keskin,  Refik},
     title = {Integer solutions of some {Diophantine} equations via {Fibonacci} and {Lucas} numbers},
     journal = {Journal of integer sequences},
     year = {2009},
     volume = {12},
     number = {8},
     zbl = {1210.11023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_8_a1/}
}
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Demirtürk,  Bahar; Keskin,  Refik. Integer solutions of some Diophantine equations via Fibonacci and Lucas numbers. Journal of integer sequences, Tome 12 (2009) no. 8. http://geodesic.mathdoc.fr/item/JIS_2009__12_8_a1/