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IMO Longlists
1966 IMO Longlists
2
The Democratic Republic Of Germany 1
The Democratic Republic Of Germany 1
Source: IMO LongList 1959-1966 Problem 2
September 1, 2004
inequalities proposed
inequalities
Problem Statement
Given
n
n
n
positive numbers
a
1
,
a_{1},
a
1
,
a
2
,
a_{2},
a
2
,
.
.
.
,
...,
...
,
a
n
a_{n}
a
n
such that
a
1
⋅
a
2
⋅
.
.
.
⋅
a
n
=
1.
a_{1}\cdot a_{2}\cdot ...\cdot a_{n}=1.
a
1
⋅
a
2
⋅
...
⋅
a
n
=
1.
Prove
(
1
+
a
1
)
(
1
+
a
2
)
.
.
.
(
1
+
a
n
)
≥
2
n
.
\left( 1+a_{1}\right) \left( 1+a_{2}\right) ...\left(1+a_{n}\right) \geq 2^{n}.
(
1
+
a
1
)
(
1
+
a
2
)
...
(
1
+
a
n
)
≥
2
n
.
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