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National and Regional Contests
Turkey Contests
National Olympiad First Round
2010 National Olympiad First Round
34
Turkey NMO 2010 1st Round - P34 (Number Theory)
Turkey NMO 2010 1st Round - P34 (Number Theory)
Source:
July 27, 2012
modular arithmetic
Problem Statement
Which one divides
2
2
2010
+
2
2
2009
+
1
2^{2^{2010}}+2^{2^{2009}}+1
2
2
2010
+
2
2
2009
+
1
?
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A
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19
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B
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17
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C
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13
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D
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11
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E
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None
<span class='latex-bold'>(A)</span>\ 19 \qquad<span class='latex-bold'>(B)</span>\ 17 \qquad<span class='latex-bold'>(C)</span>\ 13 \qquad<span class='latex-bold'>(D)</span>\ 11 \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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19
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B
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17
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C
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13
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D
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11
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E
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None
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