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National and Regional Contests
Vietnam Contests
Vietnam Team Selection Test
2010 Vietnam Team Selection Test
3
VN TST 2010 Pro 6
VN TST 2010 Pro 6
Source:
October 24, 2010
algebra
polynomial
modular arithmetic
number theory unsolved
number theory
Problem Statement
Let
S
n
S_n
S
n
ā
be sum of squares of the coefficient of the polynomial
(
1
+
x
)
n
(1+x)^n
(
1
+
x
)
n
. Prove that
S
2
n
+
1
S_{2n} +1
S
2
n
ā
+
1
is not divisible by
3.
3.
3.
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