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# Divisibility in generalized Fibonacci sequences

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### Abstract

We study the divisibility in generalized Fibonacci sequences $$(G_n)_{n\ge0}$$ defined by $$G_0=0$$, $$G_1=1$$ and $$G_n=pG_{n-1}+qG_{n-2}$$ for $$n\ge2$$, where $$p,q$$ are given integers. As corollaries, we give some divisibility properties on some well known sequences.

### Author and article information

###### Journal
14 March 2020
###### Article
2003.06643