Geodesic
Integer solutions of some Diophantine equations via Fibonacci and Lucas numbers
Journal of integer sequences, Tome 12 (2009) no. 8.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Demirt\"urk, Bahar and Keskin, Refik},
     title = {Integer solutions of some {Diophantine} equations via {Fibonacci} and {Lucas} numbers},
     journal = {Journal of integer sequences},
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     number = {8},
     year = {2009},
     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/