Identities for products and squares of \((s,t)\)-Fibonacci and \((s,t)\)-Lucas numbers
type: Item
instance of: scholarly article
zbMATH Open document ID: 1423.11033
DOI: 10.17654/MS099050743
author: Zvonko Čerin
author: Gian Mario Gianella
publication date: 2016-03-30T00:00:00Z
full work available at URL: 9603.htm
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 6561027
zbMATH Keywords: generalized Fibonacci numbers
zbMATH Keywords: generalized Lucas numbers
zbMATH Keywords: squares
zbMATH Keywords: products
zbMATH Keywords: identity
MaRDI profile type: Publication
OpenAlex ID: W2519156943
title: Identities for products and squares of \((s,t)\)-Fibonacci and \((s,t)\)-Lucas numbers
published in: Far East Journal of Mathematical Sciences
review text: The Tribonacci sequence $\{ T_n \}_{n \geq 0}$ is given byNEWLINE\[CARRIAGE_RETURNNEWLINET_0 = 0, \ T_1 = T_2 = 1, \ T_{n+3} = T_{n+2} + T_{n+1} + T_nCARRIAGE_RETURNNEWLINE\]NEWLINEfor each natural number $n \geq 0$.NEWLINENEWLINEIn the paper, the following very interesting result is proved.NEWLINEFor each squarefree integer $d \not\in \{2, 3, 5, 15, 26\}$, the Pell equation $X^2 - dY^2 = \pm 1$ has at least two positive integer solutions $(X, Y)$ and $(X', Y')$ such that both $X$ and $X'$ are sums of two Tribonacci numbers.
reviewed by: Krassimir Atanassov
description: scientific article; zbMATH DE number 6561027