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National and Regional Contests
Azerbaijan Contests
Azerbaijan EGMO TST
2017 Azerbaijan EGMO TST
2
Sequence
Sequence
Source:
August 16, 2016
algebra
Sequence
induction
Problem Statement
Let
(
a
n
)
n
≥
0
(a_n)_n\geq 0
(
a
n
)
n
≥
0
and
a
m
+
n
+
a
m
−
n
=
1
2
(
a
2
m
+
a
2
n
)
a_{m+n}+a_{m-n}=\frac{1}{2}(a_{2m}+a_{2n})
a
m
+
n
+
a
m
−
n
=
2
1
(
a
2
m
+
a
2
n
)
for every
m
≥
n
≥
0.
m\geq n\geq0.
m
≥
n
≥
0.
If
a
1
=
1
,
a_1=1,
a
1
=
1
,
then find the value of
a
2007
.
a_{2007}.
a
2007
.
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