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IMO Shortlist
1967 IMO Shortlist
6
IMO LongList 1967, Romania 6
IMO LongList 1967, Romania 6
Source: IMO LongList 1967, Romania 6
December 16, 2004
Inequality
polynomial
algebra
n-variable inequality
Problem Statement
Prove the following inequality:
∏
i
=
1
k
x
i
⋅
∑
i
=
1
k
x
i
n
−
1
≤
∑
i
=
1
k
x
i
n
+
k
−
1
,
\prod^k_{i=1} x_i \cdot \sum^k_{i=1} x^{n-1}_i \leq \sum^k_{i=1} x^{n+k-1}_i,
i
=
1
∏
k
x
i
⋅
i
=
1
∑
k
x
i
n
−
1
≤
i
=
1
∑
k
x
i
n
+
k
−
1
,
where
x
i
>
0
,
x_i > 0,
x
i
>
0
,
k
∈
N
,
n
∈
N
.
k \in \mathbb{N}, n \in \mathbb{N}.
k
∈
N
,
n
∈
N
.
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