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Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2007 National Olympiad First Round
10
10
Part of
2007 National Olympiad First Round
Problems
(1)
Turkey NMO 2007 1st Round - P10 (Number Theory)
Source:
10/4/2012
How many positive integers
n
<
1
0
6
n<10^6
n
<
1
0
6
are there such that
n
n
n
is equal to twice of square of an integer and is equal to three times of cube of an integer?
<
s
p
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c
l
a
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b
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>
(
A
)
<
/
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a
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0
<
s
p
a
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c
l
a
s
s
=
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>
(
B
)
<
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1
<
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l
a
s
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=
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>
(
C
)
<
/
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>
2
<
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p
a
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c
l
a
s
s
=
′
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a
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e
x
−
b
o
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′
>
(
D
)
<
/
s
p
a
n
>
3
<
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p
a
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c
l
a
s
s
=
′
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a
t
e
x
−
b
o
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d
′
>
(
E
)
<
/
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>
None of the above
<span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}
<
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c
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a
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(
A
)
<
/
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p
an
>
0
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
3
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
None of the above
geometry
3D geometry