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Baltic Way
2023 Baltic Way
2
Inequality with powers
Inequality with powers
Source: Baltic Way 2023/2
November 11, 2023
algebra
Problem Statement
Let
a
1
,
a
2
,
…
,
a
2023
a_1, a_2, \ldots, a_{2023}
a
1
,
a
2
,
…
,
a
2023
be positive reals such that
∑
i
=
1
2023
a
i
i
=
2023
\sum_{i=1}^{2023}a_i^i=2023
∑
i
=
1
2023
a
i
i
=
2023
. Show that
∑
i
=
1
2023
a
i
2024
−
i
>
1
+
1
2023
.
\sum_{i=1}^{2023}a_i^{2024-i}>1+\frac{1}{2023}.
i
=
1
∑
2023
a
i
2024
−
i
>
1
+
2023
1
.
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