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Turkey Contests
National Olympiad First Round
2012 National Olympiad First Round
2
2
Part of
2012 National Olympiad First Round
Problems
(1)
Turkish NMO First Round - 2012 Problem - 02 {Number Theory}
Source:
7/1/2012
Find the sum of distinct residues of the number
201
2
n
+
m
2
2012^n+m^2
201
2
n
+
m
2
on
m
o
d
11
\mod 11
mod
11
where
m
m
m
and
n
n
n
are positive integers.
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A
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55
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B
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46
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C
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43
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D
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39
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37
<span class='latex-bold'>(A)</span>\ 55 \qquad <span class='latex-bold'>(B)</span>\ 46 \qquad <span class='latex-bold'>(C)</span>\ 43 \qquad <span class='latex-bold'>(D)</span>\ 39 \qquad <span class='latex-bold'>(E)</span>\ 37
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46
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43
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39
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E
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37