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Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2013 National Olympiad First Round
18
18
Part of
2013 National Olympiad First Round
Problems
(1)
P18 [Number Theory] - Turkish NMO 1st Round - 2013
Source:
4/17/2013
What is remainder when the sum
(
2013
1
)
+
2013
(
2013
3
)
+
201
3
2
(
2013
5
)
+
⋯
+
201
3
1006
(
2013
2013
)
\binom{2013}{1}+2013\binom{2013}{3} + 2013^2\binom{2013}{5} + \dots + 2013^{1006}\binom{2013}{2013}
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1
2013
)
+
2013
(
3
2013
)
+
201
3
2
(
5
2013
)
+
⋯
+
201
3
1006
(
2013
2013
)
is divided by
41
41
41
?
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20
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14
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7
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D
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1
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None
<span class='latex-bold'>(A)</span>\ 20 \qquad<span class='latex-bold'>(B)</span>\ 14 \qquad<span class='latex-bold'>(C)</span>\ 7 \qquad<span class='latex-bold'>(D)</span>\ 1 \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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20
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14
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7
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D
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1
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E
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None
modular arithmetic