  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
giveformulas to calculate the $\gcd$ of those polynomials that do not satisfy
the strong divisibility property.
  Note. This paper is now published in INTEGERS.
