In this paper we shall continue to study from [4], for k = −1 and k = 5, the infinite sequences of triples A = (F2n+1, F2n+3, F2n+5), B = (F2n+1, 5F2n+3, F2n+5), C = (L2n+1, L2n+3, L2n+5), D = (L2n+1, 5L2n+3, L2n+5) with the property that the product of any two different components of them increased by k are squares. The sequences A and B are built from the Fibonacci numbers Fn while the sequences C and D from the Lucas numbers Ln. We show some interesting properties of these sequences that give various methods how to get squares from them.
@article{1312,
title = {Squares in Euler triples from Fibonacci and Lucas numbers},
journal = {CUBO, A Mathematical Journal},
volume = {15},
year = {2013},
language = {en},
url = {http://dml.mathdoc.fr/item/1312}
}
Cerin, Zvonko. Squares in Euler triples from Fibonacci and Lucas numbers. CUBO, A Mathematical Journal, Tome 15 (2013) . http://gdmltest.u-ga.fr/item/1312/