SQUARES IN EULER TRIPLES FROM FIBONACCI AND LUCAS NUMBERS

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...

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Autor principal:	Čerin,Zvonko
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2013
Materias:	D (k)-triple Fibonacci numbers Lucas numbers square symmetric sum alternating sum product component
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462013000200008
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spelling	oai:scielo:S0719-064620130002000082018-10-08SQUARES IN EULER TRIPLES FROM FIBONACCI AND LUCAS NUMBERSČerin,Zvonko D (k)-triple Fibonacci numbers Lucas numbers square symmetric sum alternating sum product component 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.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.15 n.2 20132013-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462013000200008en10.4067/S0719-06462013000200008
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	D (k)-triple Fibonacci numbers Lucas numbers square symmetric sum alternating sum product component
spellingShingle	D (k)-triple Fibonacci numbers Lucas numbers square symmetric sum alternating sum product component Čerin,Zvonko SQUARES IN EULER TRIPLES FROM FIBONACCI AND LUCAS NUMBERS
description	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.
author	Čerin,Zvonko
author_facet	Čerin,Zvonko
author_sort	Čerin,Zvonko
title	SQUARES IN EULER TRIPLES FROM FIBONACCI AND LUCAS NUMBERS
title_short	SQUARES IN EULER TRIPLES FROM FIBONACCI AND LUCAS NUMBERS
title_full	SQUARES IN EULER TRIPLES FROM FIBONACCI AND LUCAS NUMBERS
title_fullStr	SQUARES IN EULER TRIPLES FROM FIBONACCI AND LUCAS NUMBERS
title_full_unstemmed	SQUARES IN EULER TRIPLES FROM FIBONACCI AND LUCAS NUMBERS
title_sort	squares in euler triples from fibonacci and lucas numbers
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2013
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462013000200008
work_keys_str_mv	AT 268erinzvonko squaresineulertriplesfromfibonacciandlucasnumbers
_version_	1714206783967330304

SQUARES IN EULER TRIPLES FROM FIBONACCI AND LUCAS NUMBERS

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