MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2005 National Olympiad First Round
6
6
Part of
2005 National Olympiad First Round
Problems
(1)
P06 [Number Theory] - Turkish NMO 1st Round - 2005
Source:
10/26/2013
Which of the following divides
3
3
n
+
1
+
5
3
n
+
2
+
7
3
n
+
3
3^{3n+1} + 5^{3n+2}+7^{3n+3}
3
3
n
+
1
+
5
3
n
+
2
+
7
3
n
+
3
for every positive integer
n
n
n
?
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3
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5
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7
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11
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53
<span class='latex-bold'>(A)</span>\ 3 \qquad<span class='latex-bold'>(B)</span>\ 5 \qquad<span class='latex-bold'>(C)</span>\ 7 \qquad<span class='latex-bold'>(D)</span>\ 11 \qquad<span class='latex-bold'>(E)</span>\ 53
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7
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11
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53
modular arithmetic