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A combinatorial proof of a result on Generalized Lucas Polynomials

Laugier A., Saikia M. P.

Demonstratio Mathematica

2016

Vol. 49, nr 3

265--270

We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation = s + t for n≥2. The initial values are <0> = 2,<1> = s, respectively.

Location of zeros of polynomials

Zireh A.

Journal of Applied Analysis

2012

Vol. 18, nr 1

159-166

In this paper, we obtain a result concerning the location of zeros of a polynomial p(z)= αo+a1z+···+αnzn, where αi are complex coefficients and z is a complex variable. We obtain a ring shaped region containing all the zeros of a polynomial involving binomial coefficients and t,z-Fibonacci numbers. This result generalizes some well-known inequalities.

On the solutions of the difference equation xn+1 = max ...[wzór]

Yalcinkaya Ç., Kurbanli A. S.

Fasciculi Mathematici

2010

Nr 43

165-169

We study the solutions of the following difference equation ...[wzór] where initial conditions x-1and x0 are nonzero real numbers. In most of the cases we determine the solutions in function of the initial conditions x-1 and x0.

Fibonacci numbers with the Lehmer property

Luca F.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

Vol. 55, no 1

7-15

We show that if m > 1 is a Fibonacci number such that φ(m) | m - 1, where φ is the Euler function, then m is prime.