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Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2001 National Olympiad First Round
19
19
Part of
2001 National Olympiad First Round
Problems
(1)
P19 [Number Theory] - Turkish NMO 1st Round - 2001
Source:
4/20/2014
If the integers
m
,
n
,
k
m,n,k
m
,
n
,
k
hold the equation
221
m
+
247
n
+
323
k
=
2001
221m+247n+323k=2001
221
m
+
247
n
+
323
k
=
2001
, what is the smallest possible value of
k
k
k
greater than
100
100
100
?
<
s
p
a
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c
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a
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′
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a
t
e
x
−
b
o
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′
>
(
A
)
<
/
s
p
a
n
>
124
<
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c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
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>
(
B
)
<
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>
111
<
s
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a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
107
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
101
<
s
p
a
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c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
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>
None of the preceding
<span class='latex-bold'>(A)</span>\ 124 \qquad<span class='latex-bold'>(B)</span>\ 111 \qquad<span class='latex-bold'>(C)</span>\ 107 \qquad<span class='latex-bold'>(D)</span>\ 101 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
<
s
p
an
c
l
a
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=
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l
a
t
e
x
−
b
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′
>
(
A
)
<
/
s
p
an
>
124
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
111
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
107
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
101
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
None of the preceding
modular arithmetic