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there is a term in the Fibonacci sequence that is divided by $r$

Source: Moldova TST 2000

August 7, 2023
number theory

Problem Statement

Let (Fn)n∈N(F_n)_{n\in\mathbb{N}} be the Fibonacci sequence difined as F0=F1=1,Fn+2=Fn+1+Fn,∀n∈NF_0=F_1=1, F_{n+2}=F_{n+1}+F_n, \forall n\in\mathbb{N}. Show that for every nonnegative integer rr there is a term in the Fibonacci sequence that is divided by rr.
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