Geodesic
On the Representation of Fibonacci and Lucas Numbers as the Sum of Three Squares
Matematičeskie zametki, Tome 91 (2012) no. 5, pp. 711-719

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We study the problem of expressing the Fibonacci numbers and the Lucas numbers as the sum of three squares of integers. We obtain the description of all numbers admitting such a representation.
Keywords: Fibonacci numbers, Lucas numbers, sequence of residues. 
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Ya. A. Latushkin; V. N. Ushakov. On the Representation of Fibonacci and Lucas Numbers as the Sum of Three Squares. Matematičeskie zametki, Tome 91 (2012) no. 5, pp. 711-719. http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a6/