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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.

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          Most cited references 5

          • Record: found
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          Sets in which xy + k is always a square

           D Brown (1985)
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            • Record: found
            • Abstract: not found
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            On-Line Encyclopedia of Integer Sequences

             N Sloane (2020)
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              • Record: found
              • Abstract: not found
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              On Diophantine triples from Fibonacci and Lucas numbers

               Z Cerin (2020)
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                Author and article information

                Contributors
                Role: ND
                Journal
                cubo
                Cubo (Temuco)
                Cubo
                Universidad de La Frontera. Departamento de Matemática y Estadística (Temuco )
                0719-0646
                2013
                : 15
                : 2
                : 79-88
                Affiliations
                [1 ] University of Zagreb Croatia
                Article
                S0719-06462013000200008
                10.4067/S0719-06462013000200008

                http://creativecommons.org/licenses/by/4.0/

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                Categories
                MATHEMATICS
                MATHEMATICS, APPLIED

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