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Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2008 National Olympiad First Round
18
18
Part of
2008 National Olympiad First Round
Problems
(1)
Turkey NMO 2008 1st Round - P18 (Number Theory)
Source:
8/25/2012
How many positive integers
n
n
n
are there such that
n
+
n
+
n
+
n
\sqrt{n+\sqrt{n+\sqrt{n+\sqrt{n}}}}
n
+
n
+
n
+
n
is an integer?
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A
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1
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(
B
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2
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(
C
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3
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(
D
)
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Infinitely many
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E
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None of the above
<span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ \text{Infinitely many} \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}
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(
A
)
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1
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(
B
)
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2
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(
C
)
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3
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(
D
)
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Infinitely many
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(
E
)
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None of the above
quadratics