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Sequence
2016
Problem - 3943
The Fibonacci sequence
(
F
n
)
n
≥
0
is defined by the recurrence relation
F
n
+
2
=
F
n
+
1
+
F
n
with
F
0
=
0
and
F
1
=
1
. Prove that for any
m
,
n
∈
N
, we have
F
m
+
n
+
1
=
F
m
+
1
F
n
+
1
+
F
m
F
n
.
Deduce from here that
F
2
n
+
1
=
F
2
n
+
1
+
F
2
n
for any
n
∈
N
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