Squares in Euler triples from Fibonacci and Lucas numbers
-
Zvonko Cerin
cerin@math.hr
Downloads
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
Similar Articles
- Adrián Esparza-Amador, Parámetros especiales y deformaciones lineales de la familia \( (\wp(z))^2 + c \) , CUBO, A Mathematical Journal: In Press
- Pierpaolo Natalini, Paolo Emilio Ricci, Bell Polynomials and some of their Applications , CUBO, A Mathematical Journal: Vol. 5 No. 3 (2003): CUBO, Matemática Educacional
- Martin Moskowitz, Symmetric Spaces of Noncompact type , CUBO, A Mathematical Journal: Vol. 7 No. 2 (2005): CUBO, A Mathematical Journal
- Chao-Ping Chen, Ai-Qi Liu, Feng Qi, Proofs for the Limit of Ratios of Consecutive Terms in Fibonacci Sequence , CUBO, A Mathematical Journal: Vol. 5 No. 3 (2003): CUBO, Matemática Educacional
- Michael Holm, Sum and Difference Compositions in Discrete Fractional Calculus , CUBO, A Mathematical Journal: Vol. 13 No. 3 (2011): CUBO, A Mathematical Journal
- Minking Eie, Yao Lin Ong, A new approach to congruences of Kummer type for Bernoulli numbers , CUBO, A Mathematical Journal: Vol. 5 No. 2 (2003): CUBO, Matemática Educacional
- J¨orn Steuding, The Fibonacci Zeta-Function is Hypertranscendental , CUBO, A Mathematical Journal: Vol. 10 No. 3 (2008): CUBO, A Mathematical Journal
- Luiz Antonio Pereira Gomes, Eduardo Brandani da Silva, A Characterization of the Product Hardy Space 𻹠, CUBO, A Mathematical Journal: Vol. 11 No. 4 (2009): CUBO, A Mathematical Journal
- A.A. Shaikh, C.S. Bagewadi, On ð˜•(ð‘˜)-Contact Metric Manifolds , CUBO, A Mathematical Journal: Vol. 12 No. 1 (2010): CUBO, A Mathematical Journal
- Wolfgang Rump, The tree of primes in a field , CUBO, A Mathematical Journal: Vol. 12 No. 2 (2010): CUBO, A Mathematical Journal
<< < 1 2 3 4 5 6 7 8 9 10 > >>
You may also start an advanced similarity search for this article.
Downloads
Download data is not yet available.
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
Section
Articles
