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Contests
National and Regional Contests
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MAA AMC
AMC 12/AHSME
1999 AMC 12/AHSME
30
30
Part of
1999 AMC 12/AHSME
Problems
(1)
Diophantine Equation
Source:
1/11/2009
The number of ordered pairs of integers
(
m
,
n
)
(m,n)
(
m
,
n
)
for which
m
n
≥
0
mn \ge 0
mn
≥
0
and m^3 \plus{} n^3 \plus{} 99mn \equal{} 33^3 is equal to
<
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(
A
)
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2
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(
B
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3
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(
C
)
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33
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(
D
)
<
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35
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(
E
)
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99
<span class='latex-bold'>(A)</span>\ 2\qquad <span class='latex-bold'>(B)</span>\ 3\qquad <span class='latex-bold'>(C)</span>\ 33\qquad <span class='latex-bold'>(D)</span>\ 35\qquad <span class='latex-bold'>(E)</span>\ 99
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(
A
)
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2
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>
(
B
)
<
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>
3
<
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a
ss
=
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a
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−
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o
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d
′
>
(
C
)
<
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p
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>
33
<
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p
an
c
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a
ss
=
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l
a
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x
−
b
o
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d
′
>
(
D
)
<
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p
an
>
35
<
s
p
an
c
l
a
ss
=
′
l
a
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x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
99
geometry
3D geometry