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abstract: 'It is known that the greatest common divisor of two Fibonacci numbers is again a Fibonacci number. It is called the *strong divisibility property*. However, this property does not hold for every second order sequence. In this paper we study the generalized Fibonacci polynomials and classify them in two types depending on their Binet formula. We give a complete characterization for those polynomials that satisfy the strong divisibility property. We also give formulas to calculate the $\gcd$ of those polynomials that do not satisfy the strong divisibility property.'
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Rigoberto Flórez\
Department of Mathematics and Computer Science\
The Citadel\
Charleston, SC\
U.S.A.\
[rigo.florez@citadel.edu]{}\
 \
Robinson A. Higuita\
Instituto de Matemáticas\
Universidad de Antioquia\
Medellín\
Colombia\
[robinson.higuita@udea.edu.co]{}\
 \
Antara Mukherjee\
Department of Mathematics and Computer Science\
The Citadel\
Charleston, SC\
U.S.A.\
[antara.mukherjee@citadel.edu]{}

.2 in

Introduction
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It is well known that the greatest common divisor ($\gcd$) of two Fibonacci numbers is a Fibonacci number [@koshy]. Thus, $\gcd(F_m,F_n)=F_{\gcd(m,n)}$. It is called the *strong divisibility property* or *Fibonacci gcd property*. In this paper we study divisibility properties of generalized Fibonacci polynomials (GFP) and in particular we give characterization of the strong divisibility property for these polynomials.

We classify the GFP in 