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Baltic Way
2006 Baltic Way
2
Sum of squares of a_i less than 2006
Sum of squares of a_i less than 2006
Source: Baltic Way 2006
December 4, 2010
inequalities
function
inequalities proposed
Problem Statement
Suppose that the real numbers
a
i
∈
[
−
2
,
17
]
,
i
=
1
,
2
,
…
,
59
,
a_i\in [-2,17],\ i=1,2,\ldots,59,
a
i
∈
[
−
2
,
17
]
,
i
=
1
,
2
,
…
,
59
,
satisfy
a
1
+
a
2
+
…
+
a
59
=
0.
a_1+a_2+\ldots+a_{59}=0.
a
1
+
a
2
+
…
+
a
59
=
0.
Prove that
a
1
2
+
a
2
2
+
…
+
a
59
2
≤
2006
a_1^2+a_2^2+\ldots+a_{59}^2\le 2006
a
1
2
+
a
2
2
+
…
+
a
59
2
≤
2006
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