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National and Regional Contests
Moldova Contests
Moldova Team Selection Test
2000 Moldova Team Selection Test
5
5
Part of
2000 Moldova Team Selection Test
Problems
(1)
there is a term in the Fibonacci sequence that is divided by $r$
Source: Moldova TST 2000
8/7/2023
Let
(
F
n
)
n
∈
N
(F_n)_{n\in\mathbb{N}}
(
F
n
)
n
∈
N
be the Fibonacci sequence difined as
F
0
=
F
1
=
1
,
F
n
+
2
=
F
n
+
1
+
F
n
,
∀
n
∈
N
F_0=F_1=1, F_{n+2}=F_{n+1}+F_n, \forall n\in\mathbb{N}
F
0
=
F
1
=
1
,
F
n
+
2
=
F
n
+
1
+
F
n
,
∀
n
∈
N
. Show that for every nonnegative integer
r
r
r
there is a term in the Fibonacci sequence that is divided by
r
r
r
.
number theory