\vskip 1cm{\LARGE\bf GCD Property of the Generalized Star of \\
\vskip .11in
David in the Generalized Hosoya Triangle}
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\large
Rigoberto Fl\'orez\\
Department of Mathematics and Computer Science\\
The Citadel\\
Charleston, SC 29409\\
USA \\
\href{mailto:rigo.florez@citadel.edu}{\tt rigo.florez@citadel.edu} \\
\ \\
Robinson A. Higuita\\
Departamento de Matem\'aticas\\
Universidad de Antioquia\\
Medell\'in\\
Colombia\\
\href{mailto:robinharra@yahoo.es}{\tt robinharra@yahoo.es}\\
\ \\
Leandro Junes\\
Department of Mathematics, Computer Science and Information Systems\\
California University of Pennsylvania\\
California, PA  15419\\
USA \\
\href{mailto:junes@calu.edu}{\tt junes@calu.edu}
\end{center}

\vskip .2in

\begin{abstract}
The \emph{generalized Hosoya triangle}  is an arrangement of
numbers in which each entry is a product of two generalized Fibonacci
numbers. We prove the GCD property for the star  of David of length two. We give necessary and sufficient conditions such that the star  of David of length three satisfies the GCD property. We propose some open questions and a conjecture for the star  of David of length bigger than or equal to four. We also study GCD properties and modularity properties of generalized Fibonacci numbers.
\end{abstract}