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# SQUARES IN EULER TRIPLES FROM FIBONACCI AND LUCAS NUMBERS

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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.

### Translated abstract

En este artículo continuaremos el estudio de [4], para k = -1 y k = 5, las secuencias infinitas de tripletas 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) con la propiedad que el producto de dos componentes diferentes que se aumenta en k son cuadrados. Las secuencias A y B se construyen con los números de Fibonacci Fn mientras que las secuencias C y D se construyen con los números de Lucas Ln. Mostramos algunas propiedades interesantes de estas secuencias que entregan muchos métodos de cómo conseguir los cuadrados de ellos.

### Most cited references5

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### Sets in which xy + k is always a square

(1985)
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### On-Line Encyclopedia of Integer Sequences

(2020)
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• Record: found

### On Diophantine triples from Fibonacci and Lucas numbers

(2020)
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### Author and article information

###### Contributors
Role: ND
###### Journal
cubo
Cubo (Temuco)
Cubo
0719-0646
2013
: 15
: 2
: 79-88
###### Affiliations
[1 ] University of Zagreb Croatia
###### Article
S0719-06462013000200008
10.4067/S0719-06462013000200008

###### Product
Product Information: website
###### Categories
MATHEMATICS
MATHEMATICS, APPLIED

Applied mathematics, General mathematics