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.

Keywords

D(k)-triple , Fibonacci numbers , Lucas numbers , square , symmetric sum , alternating sum , product , component
  • Zvonko Cerin University of Zagreb, Kopernikova 7, 10010 Zagreb, Croatia.
  • Pages: 79–88
  • Date Published: 2013-06-01
  • Vol. 15 No. 2 (2013): CUBO, A Mathematical Journal

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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.

Issue

Vol. 15 No. 2 (2013): CUBO, A Mathematical Journal

Section

Articles