Fibonacci numbers and sets with the property $D(4)$
Dujella, Andrej ; Ramasamy, A. M. S.
Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, p. 401-412 / Harvested from Project Euclid
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It is proved that if $k$ and $d$ are positive integers such that the product of any two distinct elements of the set \[ \{F_{2k},\, 5F_{2k},\, 4F_{2k+2},\, d\} \] increased by $4$ is a perfect square, than $d=4L_{2k}F_{4k+2}$. This is a generalization of the results of Kedlaya, Mohanty and Ramasamy for $k=1$.
Publié le : 2005-09-14
Classification:  Diophantine $m$-tuple,  Fibonacci numbers,  simultaneous Pellian equations,  11D09,  11B39,  11J68 
@article{1126195344,
     author = {Dujella, Andrej and Ramasamy, A. M. S.},
     title = {Fibonacci numbers and sets with the property $D(4)$},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {11},
     number = {5},
     year = {2005},
     pages = { 401-412},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1126195344}
}

Dujella, Andrej; Ramasamy, A. M. S. Fibonacci numbers and sets with the property $D(4)$. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, pp.  401-412. http://gdmltest.u-ga.fr/item/1126195344/