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Contests
International Contests
Baltic Way
1999 Baltic Way
3
3
Part of
1999 Baltic Way
Problems
(1)
For which n does the inequality hold?
Source: Baltic Way 1999
12/23/2010
Determine all positive integers
n
≥
3
n\ge 3
n
≥
3
such that the inequality
a
1
a
2
+
a
2
a
3
+
…
a
n
−
1
a
n
≤
0
a_1a_2+a_2a_3+\ldots a_{n-1}a_n\le 0
a
1
a
2
+
a
2
a
3
+
…
a
n
−
1
a
n
≤
0
holds for all real numbers
a
1
,
a
2
,
…
,
a
n
a_1,a_2,\ldots , a_n
a
1
,
a
2
,
…
,
a
n
which satisfy
a
1
+
a
2
+
…
+
a
n
=
0
a_1+a_2+\ldots +a_n=0
a
1
+
a
2
+
…
+
a
n
=
0
.
inequalities
inequalities proposed