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1987 IMO Longlists
30
Prove that the sum is non zero
Prove that the sum is non zero
Source:
September 5, 2010
vector
algebra
polynomial
geometry unsolved
geometry
Problem Statement
Consider the regular
1987
1987
1987
-gon
A
1
A
2
.
.
.
A
1987
A_1A_2 . . . A_{1987}
A
1
A
2
...
A
1987
with center
O
O
O
. Show that the sum of vectors belonging to any proper subset of
M
=
{
O
A
j
∣
j
=
1
,
2
,
.
.
.
,
1987
}
M = \{OA_j | j = 1, 2, . . . , 1987\}
M
=
{
O
A
j
∣
j
=
1
,
2
,
...
,
1987
}
is nonzero.
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