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1969 IMO Shortlist
61
61
Part of
1969 IMO Shortlist
Problems
(1)
a_{n+1}=2a_n+2^n, prove a_n is power of 2 if n is.
Source:
10/4/2010
(
S
W
E
4
)
(SWE 4)
(
S
W
E
4
)
Let
a
0
,
a
1
,
a
2
,
⋯
a_0, a_1, a_2, \cdots
a
0
,
a
1
,
a
2
,
⋯
be determined with
a
0
=
0
,
a
n
+
1
=
2
a
n
+
2
n
a_0 = 0, a_{n+1} = 2a_n + 2^n
a
0
=
0
,
a
n
+
1
=
2
a
n
+
2
n
. Prove that if
n
n
n
is power of
2
2
2
, then so is
a
n
a_n
a
n
function
algebra
binomial theorem
number theory
power of 2
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