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Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2012 National Olympiad First Round
14
14
Part of
2012 National Olympiad First Round
Problems
(1)
Turkish NMO First Round - 2012 Problem - 14 {Number Theory}
Source:
7/1/2012
What is the sum of distinct remainders when
(
2
n
−
1
)
502
+
(
2
n
+
1
)
502
+
(
2
n
+
3
)
502
(2n-1)^{502}+(2n+1)^{502}+(2n+3)^{502}
(
2
n
−
1
)
502
+
(
2
n
+
1
)
502
+
(
2
n
+
3
)
502
is divided by
2012
2012
2012
where
n
n
n
is positive integer?
<
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(
A
)
<
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3
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(
B
)
<
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1510
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(
C
)
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1511
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(
D
)
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1514
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(
E
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None
<span class='latex-bold'>(A)</span>\ 3 \qquad <span class='latex-bold'>(B)</span>\ 1510 \qquad <span class='latex-bold'>(C)</span>\ 1511 \qquad <span class='latex-bold'>(D)</span>\ 1514 \qquad <span class='latex-bold'>(E)</span>\ \text{None}
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(
A
)
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3
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>
(
B
)
<
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>
1510
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=
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−
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(
C
)
<
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>
1511
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=
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x
−
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′
>
(
D
)
<
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>
1514
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x
−
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′
>
(
E
)
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>
None
modular arithmetic