Squares in Euler triples from Fibonacci and Lucas numbers
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Zvonko Cerin
cerin@math.hr
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Abstract
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.
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Published
2013-06-01
How to Cite
[1]
Z. Cerin, “Squares in Euler triples from Fibonacci and Lucas numbers”, CUBO, vol. 15, no. 2, pp. 79–88, Jun. 2013.
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